9.1 Multiplying and Dividing Rational Expressions

Alg 2

Lesson 9-1 Multiplying and Dividing Rational ExpressionsLesson 9-2 Adding and Subtracting Rational ExpressionsLesson 9-3 Graphing Rational FunctionsLesson 9-4 Direct, Joint, and Inverse VariationLesson 9-5 Classes of FunctionsLesson 9-6 Solving Rational Equations and Inequalities

Example 1 Simplify a Rational ExpressionExample 2 Use the Process of Elimination

Example 3 Simplify by Factoring Out –1Example 4 Multiply Rational ExpressionsExample 5 Divide Rational ExpressionsExample 6 Polynomials in the Numerator and DenominatorExample 7 Simplify a Complex Fraction

Simplify

Look for common factors.

1

1

Factor.

Simplify.Answer:

Under what conditions is this expression undefined?

A rational expression is undefined if the denominator equals zero. To find out when this expression is undefined, completely factor the denominator.

Answer: The values that would make the denominator equal to 0 are –7, 3, and –3. So the expression is undefined at y = –7, y = 3, and y = –3. These values are called excluded values.

a. Simplify

b. Under what conditions is this expression undefined?

Answer:

Answer: undefined for x = –5, x = 4, x = –4

Multiple-Choice Test Item

For what values of p is undefined?

A 5 B –3, 5 C 3, –5 D 5, 1, –3

Read the Test ItemYou want to determine which values of p make the denominator equal to 0.

Solve the Test ItemLook at the possible answers. Notice that the p term and the constant term are both negative, so there will be one positive solution and one negative solution. Therefore, you can eliminate choices A and D. Factor the denominator.

Factor the denominator.

Solve each equation.

Answer: B

Zero Product Propertyor

Multiple-Choice Test Item

For what values of p is undefined?

A –5, –3, –2 B –5 C 5 D –5, –3

Answer: D

Simplify

Factor the numeratorand the denominator.

Simplify.Answer: or –a

or

1

1

a

1

Simplify

Answer: –x

Simplify

Simplify.

Answer: Simplify.

Factor.

1 1 1 1 1 1 1

1 1 1 1 1 11

Simplify

Factor.

1 1 1 1 1 1 1

1 1 1 1 1 11

1

Answer: Simplify.

Simplify each expression.

a.

b.

Answer:

Answer:

Simplify

Answer: Simplify.

Simplify.

Factor.

1 1 1 1 1 1 1

1 1 1 1 1 11

Multiply by the reciprocal of divisor.

Simplify

Answer:

Simplify

Multiply bythe reciprocalof the divisor.

1 –1 1

1 1 1

Answer: Simplify.

Simplify

Multiply by thereciprocal of the divisor.

Simplify.Answer:

Factor.

1

1 1

1

Answer: 1

Simplify each expression.

a.

b.

Answer:

Simplify

Express as adivision expression.

Multiply by thereciprocal of divisor.

Factor.

1 1 –1

1 1 1

Simplify.Answer:

Simplify

Answer: