Find the roots of the equation (x^2+5x+4)/(x^2-3x+2)

Finding the root means finding the solution when the equation is equal to zero, so when (x^2+5x+4)/(x^2-3x+2)=0. This happens when the numerator x^2+5x+4 is equal to zero so we have to find the roots. To do this, we have to factorise x^2+5x+4 which we do by thinking what two numbers when added together equal 5 and when multiplied together equal 4, which is 4 and 1. This means that x^2+5x+4=(x+1)(x+4) which we can confirm by expanding (x+1)(x+4) using the FOIL method. This means that (x+1)(x+4)=0 which occurs when x=-1 or x=-4, and these are the roots to the original equation given in the question.