The partial fraction decomposition of 36/x2 -4 can be written in the form of f(x)/x-2 + g(x)/x+2 , where

Question

The partial fraction decomposition of 36/x² -4 can be written in the form of f(x)/x-2 + g(x)/x+2 , where

f(x)=

g(x)=

Answer 1

36 / (x² - 4) = A / (x - 2) + B / (x + 2)

36 = A(x + 2) + B(x - 2)

36 = Ax + 2A + Bx - 2B

36 = Ax+ Bx + 2A - 2B

36 = (A + B)(x) + 2A - 2B

A + B = 0

2A - 2B = 36

Can you solve for A and B and answer?