Question

Find \(\max(A,B,C,D)\) in the partial fractions expansion of
\(12\frac{x^3+4}{(x^2-1)(x^2+3x+2)} = \frac{A}{x-1} + \frac{B}{x+2} + \frac{C}{x+1} + \frac{D}{(x+1)^2}.\)

Answer 1

.

Answer 2

You can find A,B,C,D by combining the fractions on the right and then comparing the numerators on both sides to actually find A,B,C, and D

Answer 3

I used heaviside method
plugged in x=-2,-1,1,0