RatF - Multiplying and Dividing Rational Expressions Lesson
Multiplying and Dividing Rational Expressions
Thinking about operations with rational numbers, or fractions, will help us perform addition, subtraction, multiplication, and division with rational expressions. We will use examples involving fractions to help us extend our thinking into dealing with rational expressions with one or more variables. We just completed our discussion simplifying rational expressions, and now we will use that information and those skills when we are given more than one rational expression to multiply and or divide. Then, we will look at adding and subtracting rational expressions.
Many times, we need to simplify rational expressions in order to multiply and or divide them.
Consider the fraction 
In order to reduce this fraction, we can use the prime factorization. Well, when we are multiplying rational expressions we will use a "form" of "prime factorization" to multiply and then reduce to one rational expression. This form is the factorization of binomials, trinomials, and with more than 3 terms; having the form of a polynomial multiplied by a polynomial.
Simply put, when multiplying rational expressions, remember the following:
If the problem contains -
Monomials only: Multiply numerators together, multiply denominators together, then simplify.
Binomials/Trinomials: Factor everything you can FIRST, then simplify.
Division of Rational Expressions
When we are dividing rational expressions, remember to change the division problem into a multiplication problem. We create a multiplication of rational expressions problem by multiplying the first rational expression by the reciprocal of the second rational expression.
The following videos will discuss and model the concept of multiplying and dividing rational expressions with monomials, binomials, multiple variables, and other unknown expressions. After watching these teaching videos, practice items are provided for you to complete to master these concepts.
Multiplying Rational Expressions Practice
Dividing Rational Expressions Practice
It is important to master these concepts to be able to apply them to adding and subtracting rational expressions in the next lesson. Remember that you must always factor numerators and denominators to be able to "cancel" (divide to equal 1) factors.
IMAGES CREATED BY GAVS