Page 647 - Algebra 1

Example
2
632 Saxon Algebra 1
= 2(6x )+(x-1)(x+4) _2__
fractions. Add.
Expand the numerator.
2(x - 4)(x + 4) = 12x + x + 3x - 4
_2 2_ 2(x - 4)(x + 4)
= 13x +3x-4 _2_
Combine like terms in the numerator.
Using Equivalent Fractions to Add with Unlike Denominators
_2_ Add 6x +x-1.
x2 - 16 2x - 8
SOLUTION Factor each denominator.
6x2 x-1 6x2 x-1 _____
x2 -16 + 2x-8 = (x-4)(x+4) + 2(x-4)
LCD = 2(x - 4)(x + 4)
Write an equivalent fraction for each addend with the LCD as a denominator.
Math Reasoning
Analyze What does it mean to write an equivalent fraction?
2(6x2) __
x-1 · x+4 = (x-1)(x+4) ____
_ _
(x-4)(x+4) · 2 = 2(x-4)(x+4)
6x2 2
_
Multiply the numerator and denominator of the first fraction by 2.
Multiply the numerator and
2(x - 4) x + 4 2(x - 4)(x + 4) 2(6x2) + (x-1)(x+4)
denominator of the second
____ 2(x-4)(x+4) 2(x-4)(x+4)
_ fraction by x + 4 .
2(x - 4)(x + 4)
Using Equivalent Fractions to Subtract with
x+4
Write the sum of the equivalent
Example
3
_2_ Subtract 4x - 2x-5. 9x - 27 x2 - 9
Unlike Denominators
SOLUTION Factor each denominator.
4x - 2x - 5 = 4x - 2x - 5
_2 __2 __ 9x-27 x2 -9 9(x-3) (x-3)(x+3)
LCD = 9(x - 3)(x + 3)
4x (x + 3) - 9(2x - 5)
_2___ 9(x - 3)(x + 3) 9(x - 3)(x + 3)
Write the difference of the equivalent fractions.
Subtract.
Expand the numerator.
_ _
= 4x2(x + 3) - 9(2x - 5) ___
9(x - 3)(x + 3)
= 4x3 + 12x2 - 18x + 45
__ 9(x-3)(x+3)
There are no like terms, so the difference is 4x3 + 12x2 - 18x + 45 . 9(x - 3)(x + 3)