How do you express x^2 / (x-1)^3x2(x1)3 in partial fractions?

1 Answer
Jun 1, 2016

x^2/(x-1)^3 = 1/((x-1))+2/(x-1)^2+1/(x-1)^3x2(x1)3=1(x1)+2(x1)2+1(x1)3

Explanation:

The expansion for x^2/(x-1)^3x2(x1)3 is given by

x^2/(x-1)^3 = A/((x-1))+B/(x-1)^2+C/(x-1)^3x2(x1)3=A(x1)+B(x1)2+C(x1)3

reducing the right member to common denominator we have

x^2/(x-1)^3 = (A(x-1)^2+B(x-1)+C)/(x-1)^3x2(x1)3=A(x1)2+B(x1)+C(x1)3

Equating the numerators we have

x^2=A x^2+(B-2A)x+A-B+Cx2=Ax2+(B2A)x+AB+C

giving the following conditions

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

solving for A,B,C we get

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