Resolve the following expression into partial fraction: X^2/(x+1)^3

This type of problem can be done as

Let x^2/(x + 1)^3 = A/(x + 1) + B/(x + 1)^2 + C/(x + 1)^3
=> x^2 = A(x + 1)^2 + B(x + 1) + C
x = - 1 => C = 1

Comparing coefficients of x^2 and x,
A = 1 and 2A + B = 0 => B = - 2A = - 2
=> x^2/(x + 1)^3 = 1/(x + 1) - 2/(x + 1)^2 + 1/(x + 1)^3.

Which is correct and nothing is wrong in it. This is conventional approach.

However seeing that (x+1)^3 in the denominator it can be done by putting

x+ 1 = t or x= (t-1)
we get x^2/(x+1)^3 = (t-1)^2/t^3 = (t^2 - 2t + 1)/t^3 = 1/t - 2/t^2 + 1/t^3 

             = 1/(x+1) - 2/(x+1)^2 + 1/(x+1)^3

which reduces the number of steps.