Simplify fully 3/(2x + 12) - (x - 15)/(x^2 - 2x - 48)

The first step to answering this question is recognising that the denominators should be factorised to find any common factors. Factorising 3/2x+12 gives 3/2(x+6) and factorising (x-15)/(x²-2x-48) gives (x-15)/(x+6)(x-8). The student should then see that the next step would be to put them both over a common denominator so that they can then be subtracted. To do this the first term can be multiplied by (x-8)/(x-8). Then the second term can be multiplied by 2/2. Another way of saying this would be to multiply the top and the bottom of the first fraction by (x-8) and the second one by 2. This then gives 3(x-8)/2(x-8)(x+6) - 2(x-15)/2(x-8)(x+6). The student should then combine the fractions into 1 which is 3(x-8)-2(x-15)/2(x+6)(x-8). The brackets on the top should then be expanded and the expression simplified to (x+6)/2(x+6)(x-8). An easy mistake to make is to forget that the - outside and the - inside create a +. The (x+6) then cancel and the simplified expression is 1/2(x-8)