calculus two question

Question

The partial fraction decomposition of  can be written in the form of  where

f(x)=

g(x)=

h(x)=

Answer 1

f, g, and h are constants

f/x + g/x^2 + h/x+3 = x^2+50/x^3+3x^2

fx(x+3) + g(x+3) + hx^2 = x^2 + 50

f + h = 1

3f + g = 0

3g = 50

g = 50/3

f = -50/9

h = 59/9

f(x) = -50/9

g(x) = 50/3

h(x) = 59/9