Question: (x-5)/{(x-2)(x+1)} = A/(x-2) + B/(x+1) write the partial fraction decomposition.
(x-5)/{(x-2)(x+1)} = A/(x-2) + B/(x+1) -- multiply both sides by (x-2)(x+1)
(x - 5) = A(x + 1) + B(x - 2)
x = -1: -6 = 0 + B(-3) => B = 2
x = 2: -3 = A(3) + 0 => A = -1
The partial fraction decomposition is: -1/(x-2) + 2/(x + 1)