Topic 1: The Fundamental Counting Principle

Rational ExpressionsTopic 2: Multiplying and Dividing Rational ExpressionsI 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.ExploreHow 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 NPVs of anything that shows up at any time in the denominator.InformationThe 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 1Simplify the following products.

a)Simplifying a product

Make sure you find NPVs BEFORE you start multiplying!

Example 1Simplify the following products.

b) c)

Simplifying a product

Make sure you find NPVs BEFORE you start multiplying!

Example 1d)

Simplifying a product

Make sure that you factor first!

Make sure you find NPVs BEFORE you start multiplying!

Example 2Simplify the following quotients.

a)Simplifying a quotient

Make sure you find NPVs 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 NPVs.

Hint: You can reduce a fraction in your calculator by pressing Math 1: Frac10Example 2Simplify the following quotients.

b)

Simplifying a quotient

Make sure that you factor first!Make sure you find NPVs (in all three places) BEFORE you start multiplying!Start by re-writing the multiplication statement as a division statement!

Example 2Simplify the following quotients.

c)

Simplifying a quotient

Make sure that you factor first!Make sure you find NPVs (in all three places) BEFORE you start multiplying!Start by re-writing the multiplication statement as a division statement!

Example 2d)

Simplifying a quotient

Make sure that you factor first!Make sure you find NPVs (in all three places) BEFORE you start multiplying!Start by re-writing the multiplication statement as a division statement!

Example 3Simplify the following expressions.a)

Simplifying an expression containing several binomials

Make sure that you factor first!Make sure you find NPVs (in all three places) BEFORE you start multiplying!Start by re-writing the multiplication statement as a division statement!

Example 3Simplify the following expressions.b)

Simplifying an expression containing several binomials

Make sure that you factor first!Make sure you find NPVs (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 ExpressionsFactor all numerators, if possible.Factor all denominators, if possible.Identify the NPVs of the variable.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.Factor all numerators, if possible.Factor all denominators, if possible.Identify the NPVs of the variable.Simplify if possible.Multiply the 1st rational expression by the reciprocal of the 2nd.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 KnowAny 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.

Youre ready! Try the homework from this section.