Page 648 - Algebra 1

Example
4
Adding and Subtracting with Unlike Denominators
a. Add -35 + -6x-2 . ___
Caution
Before factoring, write expressions in descending order.
56-7x x2 -6x-16 SOLUTION
-35 + -6x-2 ___
56-7x x2 -6x-16
= -35 + -6x - 2
___ -7(x - 8) (x - 8)(x + 2)
LCD = -7(x - 8)(x + 2)
-35(x + 2) + -7(-6x - 2)
____ -7(x - 8)(x + 2) -7(x - 8)(x + 2)
= -35(x + 2) + (-7)(-6x - 2) ___
=
=
-7(x - 8)(x + 2) 7x - 56
__ -7(x - 8)(x + 2)
Factor each denominator. Find the LCD.
Write each fraction as an equivalent fraction.
Add.
Expand the numerator and collect like terms.
Factor the numerator. Divide out common factors.
Factor each denominator.
Find the LCD. Writeeachfractionasanequivalentfraction.
Subtract. Expandthenumerator. Collect like terms.
Divide out common factors.
7(x - 8) __
-7(x - 8)(x + 2) 1
Hint
Always check to see if the numerator of the sum can be factored and if a common factor can be divided out.
= -_x + 2
__
b. Subtract x-5 - x-7 .
2x - 6 x-5 - x-7
4x - 12
SOLUTION
__
2x - 6 4x - 12
= x - 5 - x - 7 __
2(x - 3) 4(x - 3) LCD = 4(x - 3)
2(x-5)- (x-7) __
4(x - 3) 4(x - 3) = 2(x-5)-1(x-7)
__ 4(x - 3)
= 2x-10-x+7 _ _
4(x - 3) = x - 3
4(x - 3)
= _1 4
Lesson 95 633