Multiply and divide rational expressions with monomial numerators and denominators

The  exercise appears under the Algebra II Math Mission. This exercise practices multiplying and dividing rational expressions with monomial numerators and denominators.

Types of Problems
There are two types of problems in this exercise:


 * 1) Multiply/Divide and simplify the rational expression, and answer if resulting expression is defined for $$x=0$$: This problem provides two rational expressions. The student is asked to correctly simplify the ratio and answer if the resulting expressionis  defined for $$x=0$$.[[File:Multiply and divide rational expressions with monomial numerators and denominators2.PNG|thumb|'Multiply/Divide and simplify the rational expression, and answer if resulting expression defined for $$x=0$$]]
 * 2) Find the student(s) that wrote an equivalent expression: This problem provides a rational expression. The student is asked to correctly find which student(s) correctly wrote an equivalent expression.

Strategies
Knowledge of fractions and factoring are encouraged to ensure success while done exercise.
 * 1) In these problems, there is a common factor that can be divided out of all four terms in the ratio.
 * 2) A monomial can be factored out of the numerator and the denominator.
 * 3) There are no restrictions needed on this exercise because the variable is assumed to be non-zero in general.
 * 4) Finding the GCF of all the terms can increase efficiency.

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=rate*time ($$d=r\times t$$) problems.