Page 55 - MarceAlgebra Demystified

42 CHAPTER 2 Introduction to Variables

18x 2 18x 2 18 2 36
3: ¼ ¼ ¼
19 11x 19 11x 19 11 209
5x 4y 20xy
4: ¼
9 3 27
At times, especially in calculus, you might need to write a fraction as a
product of two fractions or of one fraction and a whole number or of
one fraction and a variable. The steps you will follow are the same as
in multiplying fractions—only in reverse.

Examples

3 3 1 3 1 1
¼ ¼ ¼ 3
4 1 4 1 4 4
1 1
(This expression is different from 3 ¼ 3 þ :Þ
4 4
x 1 x 1 x 1
¼ ¼ ¼ x
3 3 1 3 1 3

3 3 1 3 1 1
¼ ¼ ¼ 3
x 1 x 1 x x
7 7 1 7 1
¼ ¼
8x 8 x 8 x
7x 7 x 7
¼ ¼ x
8 8 1 8
x þ 1 1 ðx þ 1Þ 1
¼ ¼ ðx þ 1Þ
2 2 1 2
2 2 1 2 1 1
¼ ¼ ¼ 2
x þ 1 1 ðx þ 1Þ 1 x þ 1 x þ 1

Practice
Separate the factor having a variable from the rest of the fraction.
4x
1: ¼
5