Simplifying rational expressions 4

The  exercise appears under the Algebra II Math Mission. This exercise practices simplification of fractions and factoring polynomials.

Types of Problems
There is one type of problem in this exercise:


 * 1) Simplify the ratio of polynomials: This problem has a ratio of polynomials that can be simplified. The student is asked to correctly simplify the ratio and provide the restriction on the domain of the expression if any exist.Sre4-1.png

Strategies
Knowledge of fractions and factoring are encouraged to ensure success on this exercise.
 * 1) There are two major subproblems here.
 * 2) One will involve factoring cubic polynomials in the numerator and denominator. In this case there is a monomial that will factor out immediately.
 * 3) One will involve factoring quadratics that have leading coefficients other than one.
 * 4) The polynomials are monic, that is, their leading coefficient is one.
 * 5) There will be restrictions on this exercise. The restriction will be the zero of any factors that are cancelled out.
 * 6) Answers can be left in factored or expanded form for full credit.

Real-life Applications

 * 1) Rational expressions are an abstraction of fractions and will increase proficiency with fractions.
 * 2) Rational equations occur in "Work rate problems" and distance=ratextime problems.