The same rules apply for algebraic fractions as for normal fractions
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When adding or subtracting, make a common denominator.
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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.
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When dividing fractions, invert the dividing fraction and multiply.
Example: Add and simplify
Notice first that
factorises into
The question becomes
Example: Add and simplify if possible:
No further simplification is possible.
Example: Multiply
by
factorises:
Hence
since the
and
terms cross cancel.
Example: Divide
by
factorises:
Hence
Since the
terms cross cancel.