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 x – 3

EXAMPLE#3 Simplify. Identify any x -values for which the expression is undefined. 6 x x 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 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 ÷

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 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 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 in your book page324

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

CLOSURE Today we learned about multiplying and idviding rational expressions