Mathematics III Exercises
This page has all the exercises currently under the Mathematics III Mission on Khan Academy.
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All items (242)
A
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Add and subtract polynomials with one variable
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Add and subtract rational expressions with factored denominators
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Add and subtract rational expressions with relatively prime denominators
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Adding and subtracting complex numbers
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Adding and subtracting negative fractions
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Adding and subtracting polynomials
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Adding and subtracting radicals
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Adding and subtracting rational expressions 1
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Adding and subtracting rational expressions 2
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Adding and subtracting rational expressions 3
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Adding and subtracting rational expressions 4
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Adding and subtracting rational expressions 5
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Adding and subtracting rational expressions 6
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Adding and subtracting rational expressions 7
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Adding and subtracting vectors in rectangular form
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Adding vectors in magnitude and direction (answer in component form)
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Adding vectors in magnitude and direction form
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Advanced structure in expressions
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Algebraically finding inverses
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Analyze extraneous solutions of radical equations
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Analyze invertible and non-invertible functions
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Analyze the solutions of systems of equations graphically
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Approximating square roots
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Arithmetic series
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Asymptotes of a hyperbola
C
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Calculating finite geometric series
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Checking solutions to two-variable linear equations
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Classify complex numbers
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Combinations
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Compare features of functions
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Compare the growth rates of exponentials and polynomials
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Comparing features of functions
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Completing solutions of systems of inequalities
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Complex number polar form intuition
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Components of vectors
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Compose functions
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Construct basic exponential functions from the initial value and the common ratio
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Constructing linear and exponential functions
D
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Defined and undefined matrix operations
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Degrees to radians
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Dependent probability
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Determinant of a 2x2 matrix
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Determinant of a 3x3 matrix
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Determine if a function is even or odd from its graph
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Determine the domain of advanced functions
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Determine the domain of advanced piecewise functions
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Determine the end behavior of rational functions
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Distance and midpoint on the complex plane
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Distinguish between direct and inverse variation
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Distinguish between linear and exponential models
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Divide polynomials by linear binomials with remainders
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Divide polynomials by monomials with remainders
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Divide polynomials with remainders
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Dividing complex numbers
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Dividing polynomials by binomials 1
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Dividing polynomials by binomials 2
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Dividing polynomials by binomials 3
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Domain and range from graph
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Domain and range with inverse functions
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Domain of a function
E
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Equation of a circle in factored form
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Equation of a circle in non-factored form
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Equations with parentheses
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Equivalent expressions with distribution and combining like terms
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Equivalent forms of exponential expressions
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Equivalent forms of expressions with complex numbers
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Equivalent forms of polynomial expressions
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Evaluate composite functions from formulas
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Evaluate composite functions from graphs and tables
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Evaluate functions from their formula
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Evaluate logarithms using the change of base rule
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Evaluating composite functions
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Evaluating expressions with variables word problems
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Evaluating function expressions
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Evaluating logarithms (advanced)
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Evaluating logarithms (basic)
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Experimental probability
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Explicit formulas for arithmetic sequences
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Explicit formulas for geometric sequences
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Exploring the foci of an ellipse
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Extraneous solutions to radical equations
F
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Factor polynomials with special product forms
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Factoring differences of squares
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Factoring polynomials by grouping
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Factoring quadratics 1
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Factoring quadratics 2
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Factoring simple special products
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Find any term of a geometric sequence, given the formula of the sequence
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Find conjugates of complex numbers
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Find inverses of polynomial, radical, and rational functions
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Find recursive formulas for geometric sequences
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Find special products of binomials (advanced)
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Find the absolute value of complex numbers
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Find the next term of a geometric sequence, given the first few terms
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Find the next term of an arithmetic sequence, given the first few terms
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Finding limits numerically
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Finite geometric series word problems
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Fractional exponents 2
G
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Geometric transformations with matrix multiplication
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Graph quadratic functions in all forms
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Graphing circles
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Graphing circles 2
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Graphing parabolas in all forms
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Graphing systems of inequalities and checking solutions
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Graphs of exponential functions
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Graphs of exponentials and logarithms
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Graphs of piecewise nonlinear functions
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Graphs of polynomials
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Graphs of square root functions
I
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Identify and analyze discontinuities of rational functions
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Identifying terms, factors, and coefficients in expressions
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Independent probability
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Infinite geometric series
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Interpret the end behavior of modeling functions
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Interpreting graphs word problems
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Intersecting functions
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Inverse of a 3x3 matrix
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Inverses of linear functions
M
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Making use of structure 2 - Factoring polynomials with special product forms
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Manipulating fractional exponents
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Match graphs of rational functions to their formula
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Category:Mathematics III: Advanced equations & functions
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Category:Mathematics III: Exponential & logarithmic functions
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Category:Mathematics III: Normal distributions
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Category:Mathematics III: Polynomial expressions, equations, & functions
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Category:Mathematics III: Radical equations & functions
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Category:Mathematics III: Rational expressions, equations, & functions
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Category:Mathematics III: Series
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Category:Mathematics III: Study Design
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Category:Mathematics III: Trigonometric functions
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Matrix addition and subtraction
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Matrix dimensions
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Matrix transpose
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Midline of trigonometric functions
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Model real-world situations with arithmetic and geometric sequences
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Model situations by combining functions using arithmetic operations
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Model situations by composing functions
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Modeling with combined functions
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Modeling with exponential functions
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Modeling with sequences
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Multiply and divide advanced rational expressions
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Multiply and divide rational expressions with polynomial numerators and denominators
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Multiply complex numbers by real or imaginary numbers
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Multiplying a matrix by a matrix
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Multiplying and dividing complex numbers in polar form
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Multiplying and dividing rational expressions 1
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Multiplying and dividing rational expressions 3
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Multiplying and dividing rational expressions 4
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Multiplying and dividing rational expressions 5
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Multiplying binomials 2
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Multiplying binomials by polynomials
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Multiplying complex numbers
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Multiplying polynomials
P
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Parabola intuition 1
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Parabola intuition 2
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Parabola intuition 3
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Partial fraction expansion
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Period of trigonometric functions
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Permutations
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Permutations and combinations
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Plot complex numbers on the complex plane
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Polynomial identities
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Powers of complex numbers
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Probabilities of compound events
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Probability with permutations and combinations
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Properties of matrix multiplication
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Prove polynomial identities
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Pythagorean theorem
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Pythagorean theorem and the equation of a circle
R
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Radical equations
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Range of a function
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Real and imaginary parts of complex numbers
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Recognizing features of functions
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Recognizing functions from graphs
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Recognizing vector quantities
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Rectangular and polar forms of complex numbers
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Recursive formulas for arithmetic sequences
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Remainder theorem of polynomials
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Representing relationships with matrices
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Rewriting and interpreting exponential functions
S
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Scalar matrix multiplication
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Scaling vectors
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Shift functions
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Shifting and reflecting functions
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Simple probability
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Simplify powers of the imaginary unit
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Simplify rational expressions by canceling binomial factors
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Simplify rational expressions by canceling monomial factors
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Simplify rational expressions using advanced factorization methods
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Simplify square roots of negative numbers
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Simplifying rational expressions 2
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Simplifying rational expressions 3
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Solve equations with two rational expressions
