section 2 multiplying and dividing rational functions chapter 5

S E C T I O N 2 M U LT I P LY I N G A N D D I V I D I N G R A T I O N A L F U N C T I O N S

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.

10x8

6x4

The expression is undefined at x = 0 because this value of x makes 6x4 equal 0

EXAMPLE#2

• Simplify. Identify any x-values for which the expression is undefined.

x2 + x – 2 x2 + 2x – 3

EXAMPLE#3

• Simplify. Identify any x-values for which the expression is undefined.

6x2 + 7x + 2

6x2 – 5x – 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.

4x – x2

x2 – 2x – 8

EXAMPLE#5

• Simplify . Identify any x values for which the expression is undefined

10 – 2x

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.

3x5y3

2x3y7

10x3y4

9x2y5

EXAMPLE#7

• Multiply. Assume that all expressions are defined

x – 3

4x + 20

x + 5

x2 – 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.

5x4

8x2y2÷

8y5

15

EXAMPLE#9

• Divide. Assume that all expressions are defined.

x4 – 9x2

x2 – 4x + 3 ÷

x4 + 2x3 – 8x2

x2 – 16

EXAMPLE#10

• Divide. Assume that all expressions are defined.

x2

4÷

12y2

x4y

STUDENT GUIDED PRACTICE

• Do 11-13 in your book page 324

EXAMPLE#11

• Solve. Check your solution.

x2 – 25

x – 5 = 14

EXAMPLE#12

• Solve. Check your solution.

x2 – 3x – 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