Fractions with Brackets

When the numerator or denominator of a fraction has two or more terms, it is important to insert a bracket e.g.

\( \frac{(3x \: + \: 2)}{5}, \frac{3}{(x\: + \: 5)}, \scriptsize etc. \)

Example 5.2.1:

Simplify the following

(a) \( \frac{x \: – \: 2}{3} \: + \: \frac{x \: + \: 3}{2} \)

(b) \( \scriptsize 5t \: – \: \normalsize \frac{3t \: – \: 2}{4} \)

(c) \( \frac{4m \: – \: 3n}{10} \: – \: \frac{2m \: – \: n}{15} \)

Solution

a. \( \frac{x \: – \: 2}{3} \: + \: \frac{x \: + \: 3}{2} \)

Denominators = 3 and 2

2	3	2
3	3	1
	1	1

L.C.M of 3 and 2 = 2 × 3 = 6

L.C.M = 6