Year 10 Interactive Maths - Second Edition

Addition and Subtraction of Algebraic Fractions

To add or subtract algebraic fractions:

• Find the lowest common multiple of the denominators.
• Express all fractions in terms of the lowest common denominator.
• Simplify the numerators to obtain the numerator of the answer.

Example 9

Solution:

Often, we set out the solution as follows:

Example 10

Solution:

Note:

• Be careful of a minus sign before a bracket.
• Factorise the final answer to discover whether any common factor exists which may be cancelled.
• Always reduce the final answer to its lowest terms.

Example 11

Solution:

Useful Device

Sometimes we use:

to simplify algebraic expressions.

Example 12

Solution:

Note:

• Always be ready to use a – b = –(b – a).
• Leave the lowest common denominator in factorised form.