How do you express #(x^2 + 5x - 7 )/( x^2 (x+ 1)^2)# in partial fractions?

1 Answer
Nov 4, 2016

Answer:

The answer is #=-7/x^2+19/x-11/(x+1)^2-19/(x+1)#

Explanation:

#(x^2+5x-7)/(x^2(x+1)^2)=A/x^2+B/x+C/(x+1)^2+D/(x+1)#
#(A(x+1)^2+Bx(x+1)^2+Cx^2+Dx^2(x+1))/(x^2(x+1)^2)#

#x^2+5x-7=A(x+1)^2+Bx(x+1)^2+Cx^2+Dx^2(x+1)#
let #x=0# #=>##-7=A#
#x=-1##=>##-11=C#
coefficentsof #x^2# #=>##1=A+2B+C+D#
coefficients of #x##=>##5=2A+B##=>##B=19#
#:.D=-19#
So, #(x^2+5x-7)/(x^2(x+1)^2)=-7/x^2+19/x-11/(x+1)^2-19/(x+1)#