Multiplication of Rational Expressions
The rules for multiplying and dividing rational expressions are the same as the rules for multiplying and dividing rational numbers, so let’s start by reviewing multiplication and division of fractions. When we multiply two fractions we multiply the numerators and denominators separately:
Multiplying Rational Expressions Involving Monomials
Multiplying Rational Expressions Involving Polynomials
When multiplying rational expressions involving polynomials, first we need to factor all polynomial expressions as much as we can. Then we follow the same procedure as before.
Multiplying a Rational Expression by a Polynomial
When we multiply a rational expression by a whole number or a polynomial, we can write the whole number (or polynomial) as a fraction with denominator equal to one. We then proceed the same way as in the previous examples.
Multiply the following rational expressions and reduce the answer to lowest terms.
x32y3⋅2y2x 2xy2⋅4y5x 2xy⋅2y2x3 4y2−1y2−9⋅y−32y−1 6aba2⋅a3b3b2 33a2−5⋅2011a3 2x2+2x−24x2+3x⋅x2+x−6x+4 xx−5⋅x2−8x+15x2−3x 5x2+16x+336x2−25⋅(6x2+5x) x2+7x+10x2−9⋅x2−3x3x2+4x−4 x2+8x+167x2+9x+2⋅7x+2x2+4x
To view the Review answers, open this PDF file and look for section 12.8.