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=PR QSQS Where neither Q or S equal zero. Steps for Multiplying Rational Expressions 1.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 2x 3 *10y 5y 2 3x 2 = 2* x* x*x*2 * 5 *y 5* y * y3*x*x =4x 3y

More Practice with multiplication x*6x-18 x 2 -3x9x

Dividing Rational Expressions For polynomials P, Q, R, and S…. P ÷ R=P*S=PS QSQRQR Steps for Dividing Rational Expressions 1.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 3x 2 ÷9x 2 y 2 8x 3 y4y 4 3x 2 *4y 4 8x 3 y9x 2 y 2 3*x*x*2*2*y*y*y*y 2*2*2*x*x*x*y3*3*x*x*y*y y 6x 3

More practice with division 2x 2 +4xy÷4x+8y 9x-18y3x-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) = x 2 -3x-10g(x) = x 2 -4x-5 x+1 x-5 What values would make one of these functions undefined? h(x)= x 2 -3x-10*x 2 -4x-5 x+1 x-5 h(x)= (x-5)(x+2)*(x+1)(x-5) x+1 x-5 h(x)= (x-5)(x+2) What is h(0)? What is h(1)?

Another example f(x)= x 2 -2x-8 g(x)= x 2 -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)?