Write x/(x-1) - x/(x+1) as a single fraction in its simplest form (Edexcel GCSE 2016)

The key concept to answering this question is to notice that you need a common denominator for both fractions in order to subtract and simplify them. Clearly the two denominators: (x-1) and (x+1) are not the same, so as it stands we cannot subtract the two fractions. As such, we have to find a denominator which is the same for both. An easy way of finding a common denominator is to multiply both denominators together to give a common denomator of: (x-1)(x+1). In order to achieve this we multiply the left fraction by (x+1)/(x+1) and the right fraction by (x-1)/(x-1). Notice also that this is the equivalent to multiplying the individual fractions by 1, which ensures the value has not changed.This allows us to achieve our common denominator of (x-1)(x+1). Now that we have a common denomator, the next steps should simply be a matter of subtracting and cancelling the terms in order to simplify the fraction. x(x+1) / ((x-1)(x+1)) - x(x-1) / ((x-1)(x+1)) = (x^2 + x) - (x^2 + x) / ((x-1)(x+1)) = 2x / ((x-1)(x+1))