How do I write this in partial fraction decomposition? x2/x^2+2x-15

Question

please help me figure this out before my final

Answer 1

Since the numerator and denominator have the same degree, divide first to get:

x² / (x² + 2x - 15) = 1 + (-2x + 15) / [(x+5)(x-3)]

(-2x + 15) / [(x+5)(x-3)] = A / (x+5) + B / (x-3)

-2x + 15 = A(x-3) + B(x+5)

If x = 3, we get 9 = 8B. So, B = 9/8

If x = -5, we get 25 = -8A. So, A = -25/8

x² / (x² + 2x - 15) = 1 - 25 / [8(x+5)] + 9 / [8(x-3)]