Algebra 2A

7.2: Multiplication and Division of Rational Expressions

September 25, 2007

Objectives

• Multiply and divide rational expressions.

• Multiply and divide two rational functions.

Multiplying Rational expressions

For polynomials P, Q, R, and S…P * R = PRQ S QSWhere neither Q or S equal zero.

Steps for Multiplying Rational Expressions1. Write each numerator and denominator in completely

factored form.2. Divide by any common factors in both the numerator

and the denominator.3. Multiply as needed to form the desired product.

Practice with Multiplication

2x3 * 10y

5y2 3x2

= 2* x* x*x * 2 * 5 *y

5* y * y 3*x*x

=4x

3y

More Practice with multiplication

x * 6x-18

x2-3x 9x

Dividing Rational Expressions

For polynomials P, Q, R, and S….

P ÷ R = P * S = PSQ S Q R

QR

Steps for Dividing Rational Expressions1. Invert the second rational expression (the divisor)

to write the problem as a multiplication problem.2. Proceed as if you are doing multiplication.

Practice with division

3x2 ÷ 9x2y2

8x3y 4y4

3x2 * 4y4

8x3y 9x2y2

3*x*x * 2*2*y*y*y*y2*2*2*x*x*x*y 3*3*x*x*y*y

y6x3

More practice with division

2x2+4xy ÷ 4x+8y

9x-18y 3x-6y

Multiplying rational functions

h(x)= f(x) * g(x)

Multiplying the functions in the same way you multiplied expressions when no value for x is specified.

When given a value for x, plug it in an solve. Watch out for values that make either function undefined.

Multiplying rational functions

h(x)= f(x) * g(x)f(x) = x2-3x-10 g(x) = x2-4x-5

x+1 x-5What values would make one of these functions undefined?h(x)= x2-3x-10 * x2-4x-5

x+1 x-5h(x)= (x-5)(x+2) * (x+1)(x-5)

x+1 x-5h(x)= (x-5)(x+2)

What is h(0)?What is h(1)?

Another example

f(x)= x2-2x-8 g(x)= x2-3x-10

x+2 x-4

What is f(0)g(0)?

What is f(4)g(4)?

What is h(x), if h(x)=f(x)g(x)?