Express (5x + 4)/(x +2)(x - 1) in partial fractions.

To put this equation into partial fractions we need to consider it in the form: (5x + 4)/(x +2)(x - 1) = A/(x + 2) + B/(x - 1) where A and B are numbers we are trying to find. To do this we need to multiply through by (x + 2)(x - 1): 5x + 4 = A(x - 1) + B(x + 2) To then find the values of A and B, we substitute in appropriate values of x, ie. x=1 and x=-2 as follows: x=1 gives: 5 + 4 = A(1 - 1) + B(1 + 2) so 9 = 3B, hence B = 3 x=-2 gives: -10 + 4 = A( -2 - 1) + B(-2 + 2) so, -6 = -3A, hence A = 2. So in partial fractions, the equation is: (5x + 4)/(x + 2)(x - 1) = 2/(x + 2) + 3/(x - 1)