section 2 multiplying and dividing rational functions chapter 5
TRANSCRIPT
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