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

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Answer 1 · 2015-12-14T03:45:40

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

#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#