Rational Expressions Topic 2: Multiplying and Dividing Rational Expressions

I can compare the strategies for performing a given operation on rational expressions to the strategies for performing the same operation on rational expressions. I can determine the non-permissible values when performing operations on rational expressions. I can determine, in simplified form, the product or quotient of two rational expressions.

Explore… Multiply the numerators and multiply the denominators. Then simplify.

Explore… Multiply the first fraction by the reciprocal of the second fraction. Then simplify.

Explore… How can you determine the non-permissible values of the variable in the product or quotient of two rational expressions? The non-permissible values can be determined by finding all NPV’s of anything that shows up at any time in the denominator.

Information The strategies used to multiply and divide rational numbers can be used to multiply and divide rational expressions. Any polynomial that ever appears in the denominator of a rational expression must be used to determine the non- permissible values of the entire rational expression.

Example 1 Simplify the following products. a) Simplifying a product Make sure you find NPV’s BEFORE you start multiplying!

Example 1 Simplify the following products. b) c) Simplifying a product Make sure you find NPV’s BEFORE you start multiplying!

Example 1 d) Simplifying a product Make sure that you factor first! Make sure you find NPV’s BEFORE you start multiplying!

Example 2 Simplify the following quotients. a) Simplifying a quotient Make sure you find NPV’s BEFORE you start multiplying! Start by re-writing the multiplication statement as a division statement! Keep in mind that both the numerator and denominator of the second rational expression were at some point in the denominator. You must check 3 places for NPV’s. Hint: You can reduce a fraction in your calculator by pressing Math 1: Frac

Example 2 Simplify the following quotients. b) Simplifying a quotient Make sure that you factor first! Make sure you find NPV’s (in all three places) BEFORE you start multiplying! Start by re-writing the multiplication statement as a division statement!

Example 2 Simplify the following quotients. c) Simplifying a quotient Make sure that you factor first! Make sure you find NPV’s (in all three places) BEFORE you start multiplying! Start by re-writing the multiplication statement as a division statement!

Example 2 d) Simplifying a quotient Make sure that you factor first! Make sure you find NPV’s (in all three places) BEFORE you start multiplying! Start by re-writing the multiplication statement as a division statement!

Example 3 Simplify the following expressions. a) Simplifying an expression containing several binomials Make sure that you factor first! Make sure you find NPV’s (in all three places) BEFORE you start multiplying! Start by re-writing the multiplication statement as a division statement!

Example 3 Simplify the following expressions. b) Simplifying an expression containing several binomials Make sure that you factor first! Make sure you find NPV’s (in all three places) BEFORE you start multiplying! Start by re-writing the multiplication statement as a division statement!

Need to Know Multiplying Rational ExpressionsDividing Rational Expressions 1.Factor all numerators, if possible. 2.Factor all denominators, if possible. 3.Identify the NPVs of the variable. 4.Simplify if possible. 5. Write the product as a single rational expression by:  multiplying numerators together.  multiplying denominators together. 6. Simplify if possible. 7. Rewrite, stating the restrictions on the variable. 1.Factor all numerators, if possible. 2.Factor all denominators, if possible. 3.Identify the NPVs of the variable. 4.Simplify if possible. 5.Multiply the 1 st rational expression by the reciprocal of the 2 nd. 6.Write the product as a single rational expression by:  multiplying numerators together.  multiplying denominators together. 7. Simplify if possible. 8. Rewrite, stating the restrictions on the variable.

Need to Know Any polynomial that ever appears in the denominator of a rational expression must be used to determine the non-permissible values of the entire rational expression. You’re ready! Try the homework from this section.