Presentation on theme: "11.5 Multiplying and Dividing Rational Expressions"— Presentation transcript:
1 11.5 Multiplying and Dividing Rational Expressions Multiply and divide rational expressions.Rules for multiplying and dividing rational expressions are the same as for multiplying and dividing fractions.
2 Multiply rational expressions involving monomials EXAMPLE 1Multiply rational expressions involving monomialsFind the product2x23x6x212x32x23x6x212x3=(2x2)(6x2)(3x)(12x3)Multiply numerators and denominators.12x436x4=Product of powers property12 x4x4=Factor and divide out common factors.13=Simplify.
4 Multiply a rational expression by a polynomial EXAMPLE 3Multiply a rational expression by a polynomialFind the product5xx2 + 5x + 6(x + 3).Rewrite polynomial as a fraction.5xx2 + 5x + 6(x + 3)=1Multiply numerators and denominators.=5x(x + 3)x2 + 5x + 6Factor and divide out common factor.=5x(x + 3)(x + 3)(x + 2)=5xx + 2Simplify.
6 Divide a rational expression by a polynomial EXAMPLE 5Divide a rational expression by a polynomialFind the quotient2x2 + 16x + 243x2(x +6).Rewrite polynomial as fraction.2x2 + 16x + 243x2(x +6).=1Multiply by multiplicative inverse.2x2 + 16x + 243x2=1(x +6).Multiply numerators and denominators.2x2 + 16x + 243x2=(x +6).Factor and divide out common factor.=2(x + 2)(x + 6)3x2(x + 6)=2(x + 2)3x2Simplify.