Rationalise and simplify (root(3) - 7)/(root(3) + 1) . Give your answer in the form a + b*root(3) where a, b are integers.

There are two ways of solving this problem, one which is the routine method that always works in these cases, and one which requires an interesting little trick.The standard method is to use the difference of two squares removing the root in the denominator, by multiplying top and bottom by root(3) - 1. Then with a bit of algebra and multiplying out brackets we arrive at our result.The nifty trick is to observe that the top part is the bottom - 8. This allows us to separate the fraction into two, neither of which has a root on the top. This makes things a lot simpler although it will still require the difference of two squares.