 ## Tutoring on Multiplying and Dividing Rational Expressions

Learning Objectives:

#### Understand to Multiply and Divide Rational Expressions.

Math Tutoring on Multiplying and Dividing Rational Expressions

Multiplying rational expressions is just like multiplying fractions. So, the basic rule is to find the product of two rational expressions, you multiply the numerators together and then you multiply the denominators together. However, by now, we know our product must be in simplified form. Let u, v, w and z represent real numbers, variables or algebraic expressions such that v ≠ 0 and z ≠ 0. Then the product u/v and w/z is   u/v •w/z = uw/vz.

So, in order to recognize the common factors in the product, we will write the numerators and denominators in factored form to simplify before we multiply.  Let's go ahead and take a look at division now. The main thing to remember about the division of rational expressions is that we convert them to multiplication. Let u, v, w, and z represent real numbers, variables or algebraic expressions such that, v ≠ 0 and z ≠ 0. Then the quotient of u/v and w/z is u/v ÷w/z = u/v • z/w = uz/vw.  So, instead of dividing by w over z, we will multiply by the reciprocal or multiply by z over w. Once we convert the problem to multiplication, we will follow the same steps as multiplication.

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Hook Questions:

1. How do you multiply and divide rational expressions?

2. What are the steps for multiplying and dividing rational expressions?

3. How do you multiply and divide rational numbers?

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