Fractions with Brackets

Topic Content:

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

L.C.M of 3 and 2 = 2 × 3 = 6

L.C.M = 6

\( \frac{x \: – \: 2}{3} \: + \: \frac{x \: + \: 3}{2} \\ = \frac{2(x \: – \:2) \: + \: 3(x \: + \: 3)}{6} \\ = \frac{2(x) \: + \: 2(-2) \: + \: 3(x) \: + \: 3(+3)}{6}\\ = \frac{2x \: – \: 4 \: + \: 3x \: + \: 9}{6} \\ = \frac{2x \: + \: 3x \: – \: 4 \: + \: 9}{6} \\ = \frac{5x \:+\: 5}{6} \)

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

= \( \frac {5t}{1} \: – \: \frac{(3t \: – \: 2)}{4} \)

L.C.M