Simplify rational expressions by canceling binomial factors

The  exercise appears under the Algebra II Math Mission. This exercise practices factoring the numerator and the denominator of a rational expression and cancel out common binomial terms.

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


 * 1) Simplify the following rational expression: This problem provides a rational expression. The student is asked to correctly simplify the ratio and provide which values would make the expression undefined.Simplify rational expressions by canceling binomial factors.PNG

Strategies
Knowledge of fractions and factoring are encouraged to ensure success while done exercise.
 * 1) Students can simplify rational expressions by finding the factors that are shared by both the numerator and the denominator, and then canceling them out. To do that, students need to factor the numerator and the denominator completely.
 * 2) Furthermore, the values of $$x$$ which make an expression undefined are precisely those values that when substituted into the expression result in a denominator equal to zero. Users can often determine these values more easily by factoring 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.