Simplify the following fraction - Numerator = 2(8-k) + 4(k-1) Denominator = k^2 - 36

The first task is to multiply out the brackets in the numerator. By doing this, we find that the numerator is equivalent to "12 + 2k". We should now simplify the denominator. We can convert it into two brackets by recognising that "k^2 -36" is the difference of two squares. Hence, we identify the square number which is 36 and so we simplify the expression to (k+6)(k-6).
We are ideally looking for a common factor in the numerator and denominator so that we can cancel them out. Therefore, we try and simplify the numerator further and we can. If we take out a common factor of 2 from "12+2k", we find that the expression is the same as "2(k+6)". Now that we have a common factor in the numerator and denominator, we can cancel the "(k+6)" out of the fraction. We are then left with the answer which is "2/k-6"