## ALGERAIC FRACTIONS

To add or subtract fractions with different denominators, first change them to equivalent fractions. This is done by finding the L C M of the denominators

**Example1**: Simplify 2a/5 + 4a/3

**Solution:**

The L C M is 15

6a + 20a/ 15 = 26a/15

**Example 2**: Simplify 3/5x + 1/2x – 1/4x

**Solution:**

Find the L C M of the expression = 20X

12 + 10 – 5 = 17/20X

## SIMPLIFYING FRACTION

**Example 1**: Reduce 25X^{4}Y^{3}/35X^{3}y^{3 }

**solution**

Divide through by 5X^{3}Y^{3}(the common factor )

= 5x/7

Example 2: Reduce 8X^{3}Y^{2}/6X^{3}Z

Solution:

Divide through by 2X ^{3}(the common factor)

4Y^{2}/3Z

__MULTIPLICATION AND DIVISION OF ALGEBRAIC FRACTION__

__MULTIPLICATION AND DIVISION OF ALGEBRAIC FRACTION__

Example 1: Simplfy (X-2)/7 * 4/(X-2)

Solution : X – 2/7 * 4/ X -2 (X-2) divides themselves

= 4/7

Example 2: Simplify 6X^{2}/11y ÷ 18X/33Y^{2 }

Solution

6X^{2}/11y * 33Y^{2}/18X (division sign change to multiplication)

= XY

__FRACTIONS WITH BRACKETS__

__FRACTIONS WITH BRACKETS__

Example1: simplify the following (a) 2x + 5/4 + 2X – 3 /4 (b) 7X – 2 /4 + X – 4 /6

Solution:

(a). The L C M is 4

(2X + 5) + ( 2X – 3)/4

4x + 2/4 = 2(2X + 1)/4

= 2X + 1/2

(b). 7X – 2 /4 + X – 4 /6

Solution:

The L C M = 12

21x – 6 + 2X – 6 – 8 / 12

= 23X – 14/ 12

See also