Page 95 - MarceAlgebra Demystified

82 CHAPTER 5 Exponents and Roots

2 2 3
5: ðx 1Þðx 1Þ ¼
2
6: ð 16x 4Þ 5 ¼

Solutions

2 3 2 3
ð5x þ x þ 1Þ ð5x þ x þ 1Þ 2 3 1
1: ¼ ¼ð5x þ x þ 1Þ
2
5x þ x þ 1 ð5x þ x þ 1Þ 1
2
2 2
¼ð5x þ x þ 1Þ
9
ð7xÞ 9 3 6
2: ¼ð7xÞ ¼ð7xÞ
3
ð7xÞ
0
3: ð2x 5Þ ¼ 1
11 6 11þ6 17
4: ðx þ 1Þ ðx þ 1Þ ¼ðx þ 1Þ ¼ðx þ 1Þ
2 2 3 2 1 2 3 2 1þ3 2 4
5: ðx 1Þðx 1Þ ¼ðx 1Þ ðx 1Þ ¼ðx 1Þ ¼ðx 1Þ
5 2 ð5Þð2Þ 10
6: ðð16x 4Þ Þ ¼ð16x 4Þ ¼ð16x 4Þ

Adding/Subtracting Fractions

When adding fractions with variables in one or more denominators, the LCD
will have each variable (or algebraic expression) to its highest power as a
1 1 1 1
2 3
factor. For example, the LCD for 2 þ þ 3 þ 2 is x y .
x x y y
Examples

4 3 4 3 x 4 3x 4 3x
¼ ¼ ¼
x 2 x x 2 x x x 2 x 2 x 2
13 6 13 z 6 xy 13z 6xy 13z 6xy
¼ ¼ ¼
2
2
2
xy 2 yz xy 2 z yz xy xy z xy z xy z