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Year 10 Interactive Maths - Second Edition


Addition and Subtraction of Algebraic Fractions

Knowledge of adding and subtracting algebraic fractions is as important as knowledge of factorisation.

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.

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