Algebraic Fractions

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The same rules apply for algebraic fractions as for normal fractions

  1. When adding or subtracting, make a common denominator.

  2. When multiplying fractions, cross cancel first if possible. Multiply the denominators together to make a new denominator. Multiply the numerators together to make a new numerator. Cancel if possible.

  3. When dividing fractions, invert the dividing fraction and multiply.

Example: Add and simplify

Notice first thatfactorises intoThe question becomes

Example: Add and simplify if possible:

No further simplification is possible.

Example: Multiplyby

factorises:

Hence

since theandterms cross cancel.

Example: Divideby

factorises:Hence

Since theterms cross cancel.

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