Question

Partial Fraction Decomposition:
(x^2 +2) / ((x-1)(x+2)^2)

Answer 1

a/(x-1) + b/(x+2) + c/(x+2)^2 = f(x)

Answer 2

compare the coefficients and obtain values of a,b,c

Answer 3

to expand on this
a(x+2)^2 + b(x-1)(x+2) +c(x-1) = x^2 + 2
a(x^2+4x+4) +b(x^2+x-2) +c(x-1) =x^2+2
(a+b)x^2 + (4a+b+c)x + (4a-2b-c) = x^2 +2
coefficient of x^2 is 1 thus a+b =1
coefficient of x is 0 thus 4a+b+c=0
leaving 4a-2b-c = 2
system of 3 equations w/ 3 variables
solve using substitution or elimination
a= 1/3
b= 2/3
c = -2