Page 286 - Algebra 1

Simplifying Using a Common Factor
Simplify each rational expression. Determine undefined values. a. _54x+9
Example
2
Caution
Determine values that cause the denominator to equal zero before the fraction is simplified.
4+x S_OLUTION
54x + 9 , x ≠ -4 4+x
4+x 4+x
9(6x + 1)
Determine undefined values.
Find the numerator’s GCF. Find the denominator’s GCF.
Factor.
Include undefined values in the answer.
Find the numerator’s GCF. Find the denominator’s GCF.
Factor. Determine undefined values.
Simplify by dividing out like monomials.
Include undefined values in the answer.
Find the numerator’s GCF. Find the denominator’s GCF.
Factor. Determine undefined values. Simplify by dividing out like binomials.
Simplify.
Include undefined values in the answer.
GCF = 9 GCF = none
54x+9 = 9(6x+1) _ _
b.
4+ _x
, x ≠ -4 2x2 - 10x
4x2 + 6x SOLUTION
GCF = 2x GCF = 2x
__
2x2 -10x = 2x(x-5) ;x≠-3;x≠0
4x2 + 6x 2x(2x + 3) 1
_ 2
2x(x - 5) __
x-5 2x(2x+3) = 2x+3
_1
x-5 ,x≠-3;x≠0
2x + 3
_ 2
_2
2x -14x
c.
4x - 28 SOLUTION
GCF = 2x GCF = 4
2x2 -14x = 2x(x-7);x≠7 __
4x - 28 4(x - 7) 2x(x-7) = 2x
_1_ 4(x - 7) 4 11
__ 2x = x
42 2
_x ; x ≠ 7 2
Lesson 43 271