simplify fully (x^2-5x+4)/(x^2-2x-8)

First we need to look at the quadratic formulas separately and factorise them. (x^2-5x+4) the sum is -5 and the product is 4, we need to find numbers that add to get -5 and multiply to get 4, which is -4, and -1. Then sub these numbers back into the equation where x is written making it x^2-x-4x+4. simplify the two terms into brackets = x(x-1)-4(x-1) and this gives the factorised version of the equation (x-1)(x-4). Do the same for the bottom equation (x^2-2x-8), the sum is -2 and the product is -8, that add to get -2 and multiply to get -8 is -4, and 2. subbing them back into x in the equation gives x^2+2x-4x-8, simplifying this by putting it into brackets gives x(x+2)-4(x+2). the factorised equation is (x-4)(x+2).when writing the equations in the fraction form = (x-1)(x-4)/(x-4)(x+2), there is a common term (x-4), which can be taken out to simplify further, leaving (x-1)/(x+2).