# SECTION 2 MULTIPLYING AND DIVIDING RATIONAL FUNCTIONS CHAPTER 5.

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SECTION 2 MULTIPLYING AND DIVIDING RATIONAL FUNCTIONS CHAPTER 5

OBJECTIVES Simplify rational expressions. Multiply and divide rational expressions.

RATIONAL EXPRESSION In the previous lesson you worked with inverse variation functions such as y = k/x. The expression on the right side of this equation is a rational expression. A rational expression is a quotient of two polynomials. Other examples of rational expressions include the following:

RATIONAL EXPRESSION Because rational expressions are ratios of polynomials, you can simplify them the same way as you simplify fractions. Recall that to write a fraction in simplest form, you can divide out common factors in the numerator and denominator. When identifying values for which a rational expression is undefined, identify the values of the variable that make the original denominator equal to 0.

EXAMPLE#1 Simplify. Identify any x -values for which the expression is undefined. 10 x 8 6x46x4 The expression is undefined at x = 0 because this value of x makes 6x 4 equal 0

EXAMPLE#2 Simplify. Identify any x -values for which the expression is undefined. x 2 + x – 2 x 2 + 2 x – 3

EXAMPLE#3 Simplify. Identify any x -values for which the expression is undefined. 6 x 2 + 7 x + 2 6 x 2 – 5 x – 6

STUDENT GUIDED PRACTICE Do problems 2 to 4in your book page 324

EXAMPLE#4 Simplify. Identify any x values for which the expression is undefined. 4 x – x 2 x 2 – 2 x – 8

EXAMPLE#5 Simplify. Identify any x values for which the expression is undefined 10 – 2 x x – 5

STUDENT GUIDED PRACTICE Do Problems 5-7 in your book page 324

RULES FOR MULTIPLYING RATIONAL FUNCTIONS You can multiply rational expressions the same way that you multiply fractions.

EXAMPLE#6 Multiply. Assume that all expressions are defined. 3 x 5 y 3 2x3y72x3y7  10 x 3 y 4 9x2y59x2y5

EXAMPLE#7 Multiply. Assume that all expressions are defined x – 3 4 x + 20  x + 5 x 2 – 9

STUDENT GUIDED PRACTICE Do problems 8 -10 in your book page 324

DIVIDING RATIONAL FUNCTIONS You can also divide rational expressions. Recall that to divide by a fraction, you multiply by its reciprocal. 1 2 3 4 ÷

EXAMPLE#8 Divide. Assume that all expressions are defined. 5 x 4 8x2y28x2y2 ÷ 8y58y5 15

EXAMPLE#9 Divide. Assume that all expressions are defined. x 4 – 9 x 2 x 2 – 4 x + 3 ÷ x 4 + 2 x 3 – 8 x 2 x 2 – 16

EXAMPLE#10 Divide. Assume that all expressions are defined. x 2 4 ÷ 12 y 2 x4yx4y

STUDENT GUIDED PRACTICE Do 11-13 in your book page 324

EXAMPLE#11 Solve. Check your solution. x 2 – 25 x – 5 = 14

EXAMPLE#12 Solve. Check your solution. x 2 – 3 x – 10 x – 2 = 7

STUDENT GUIDED PRACTICE Do problems 15-17 in your book page324

HOMEWORK Do Even problems fro 20-32 in your book page 324 and 325

CLOSURE Today we learned about multiplying and idviding rational expressions