How do you write the partial fraction decomposition of the rational expression (x^2)/(x+1)^3?

1 Answer
Dec 14, 2015

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

Explanation:

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^2=Ax^2+2Ax+A+Bx+B+C

x^2=x^2(A)+x(2A+B)+1(A+B+C)

Thus, {(A=1),(2A+B=0),(A+B+C=0):}

Solve to see that {(A=1),(B=-2),(C=1):}

Therefore,

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