Core Mathematics 3: Algebraic Fractions

Algebraic fractions can be simplified by cancelling down. To do this the numerators and denominators must be fully factorised first.
I the numerator or the denominator contain fractions you can multiply both by the same number (The lowest common multiple) to create an equivalent fraction.
To multiply fractions, you simply multiple the numerators and multiply the denominators. If possible you should cancel down first.
To divide two fractions, multiply the first fraction by the reciprocal of the second fraction.
To add (or subtract) fractions each fraction must have the same denominator. This is done by finding the lowest common multiple of denominators.
When the numerator has the same or higher degree than the denominator, you can divide the terms to produce a "mixed" number fraction. This can be done either by using long division or by using the remainder theorem: f(x)=Q(x) x Divider + Remainder. Where Q(x) is the quotient and is how many times the divisor divides into the function.

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