The partial fraction decomposition of x2 +56/x3+x2 can be written in the form of f(x)/x +g(x)/x2+h(x)/x+1,where

Question

The partial fraction decomposition of x² +56/x³+x² can be written in the form of f(x)/x +g(x)/x²+h(x)/x+1,where

f(x)=

g(x)=

h(x)=

Answer 1

(x² + 56) / (x³ + x²) = (A / x) + (B / x²) + C / (x + 1)

x² + 56 = Ax²(x + 1) + Bx(x + 1) + Cx³

x² + 56 = Ax³ + Ax² + Bx² + Bx + Cx³

x² + 56 = (A + C)x³ + (A + B)x² + Bx

A + C = 0

A + B = 1

B = 0