Presentation on theme: "11.5 Multiplying and Dividing Rational Expressions"— Presentation transcript:
111.5 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.
2Multiply 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.
4Multiply 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.
6Divide 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.