Simplifying rational expressions 2

The Simplifying rational expressions 2 exercise appears under the Algebra II Math Mission and Mathematics III Math Mission. This exercise practices simplification of fractions and factoring out monomials from polynomials by the distributive property.

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.

   

   Simplify the ratio of polynomials

Strategies

Knowledge of fractions and factoring are encouraged to ensure success on this 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.
5. 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 expressions and equations also can occur in ${\text{distance}=\text{rate}\times\text{time}}$ problems.