Page 591 - Algebra 1

L E S S O N Multiplying and Dividing Rational
88
Expressions
Warm Up
1. Vocabulary A (radical, rational) expression has at least one
(39)
Simplify. Assume that no denominator is equal to zero.
variable in its denominator.
2.x6x2 (3)
3. 8b4 _
(32) 12b9
12y - 18y _4_3
4. 2
(43) 28y - 42y
5. Factor x2 - 14x + 24. (72)
New Concepts Multiplying and dividing rational expressions follows the same procedure as multiplying and dividing fractions.
Multiplying Rational Expressions
Math Language
A polynomial is a monomial or a sum or difference of monomials.
Multiplying Rational Expressions
Dividing Rational Expressions
If a, b, c, and d are nonzero ___
polynomials, a · c = ac . b d bd
If a, b, c, and d are nonzero _____
polynomials, a÷c=a·d=ad. b d b c bc
Example
1
Find each product. _4 _22
a. 6xy·7xy 21xy3 3x3y2
SOLUTION
_4 _22 6xy ·7xy
Hint
Remember, when multiplying powers, find the sum of the exponents.
xa ·xb =xa+b When dividing powers,
subtract the exponents.
_x a a - b xb=x
21_xy3 3x3y2 42x6y3
= 63x4y5 _2
Multiply the numerators and denominators. Simplify.
= 2x 3y2
b. 6x·3x _2 _
5y4 7y2 SOLUTION
6x · 3x _2 _
5y4 7y2 _3
= 18x 35y6
Online Connection www.SaxonMathResources.com
Multiply the numerators and denominators.
There are no common factors, so the product does not simplify any further.
576 Saxon Algebra 1