Page 646 - Algebra 1

L E S S O N Combining Rational Expressions with
95
Unlike Denominators
Warm Up
1. Vocabulary One of two or more numbers or expressions that are
(2)
Find the LCM.
2. 8x4y and 12x3y2
(57)
3. (9x - 27) and (4x - 12) (57)
Factor.
4.x2 +4x-21
(72)
5.10x2 +13x-3 (75)
multiplied to get a product is called a (n) .
New Concepts The steps for adding rational expressions are the same as for adding numerical fractions. Fractions with unlike denominators cannot be added
unless you first find their least common denominator.
Finding a Common Denominator
Example
1
Find the least common denominator (LCD) for each expression. ___
Math Language
A least common denominator (LCD) is the least common multiple (LCM) of the denominators.
a. 3 - 9 (x+3) (x2 -2x-15)
SOLUTION
3-9 ___
(x+3) (x2 -2x-15) ___
= 3 - 9
(x + 3) (x + 3)(x - 5)
Factor each denominator, if possible.
To find the LCD of (x + 3) and (x + 3)(x - 5), use every factor of
each denominator the greatest number of times it is a factor of either denominator. Each denominator has a factor of (x + 3). One denominator also has a factor of (x - 5). The product of these two factors is the LCD.
LCD = (x + 3)(x - 5)
b. 2x + 12x
___ 4x2 -196 x2 +x-56
SOLUTION
2x + 12x ___
4x2 -196 x2 +x-56
= 2x + 12x
____ 4(x - 7)(x + 7) (x - 7)(x + 8)
Factor each denominator completely.
Online Connection www.SaxonMathResources.com
LCD = 4(x - 7)(x + 7)(x + 8)
Lesson 95 631