Page 52 - MarceAlgebra Demystified

CHAPTER 2 Introduction to Variables 39

2 þ x 2 x 2
¼ þ ¼ þ 1:
x x x x
Simply because a plus or minus sign appears in a fraction does not auto-
3 þ x
matically mean that canceling is not appropriate. For instance ¼ 1
3 þ x
because any nonzero quantity divided by itself is one.

Examples

ð2 þ 3xÞðx 1Þ 2 þ 3x x 1
¼ ¼ x 1:
2 þ 3x 2 þ 3x 1
The reason 2 + 3x can be canceled is that 2 + 3x is a factor of
(2 + 3x)(x 1).
2ðx þ 7Þð3x þ 1Þ 2 ðx þ 7Þð3x þ 1Þ
¼ ¼ðx þ 7Þð3x þ 1Þ
2 2 1

15ðx þ 6Þðx 2Þ 3 5ðx þ 6Þðx 2Þ 3ðx 2Þ 5ðx þ 6Þ
¼ ¼ ¼ 5ðx þ 6Þ
3ðx 2Þ 3ðx 2Þ 3ðx 2Þ 1

Practice

3xy
1: ¼
2x

8x
2: ¼
4
30xy
3: ¼
16y

72x
4: ¼
18xy

xðx 6Þ
5: ¼
2x
6xyð2x 1Þ
6: ¼
3x