How do you write the partial fraction decomposition of the rational expression # (x^2)/(x+1)^3#?
1 Answer
Mar 29, 2017
Explanation:
#x^2/(x+1)^3 = A/(x+1)+B/(x+1)^2+C/(x+1)^3#
#color(white)(x^2/(x+1)^3) = (A(x+1)^2+B(x+1)+C)/(x+1)^3#
#color(white)(x^2/(x+1)^3) = (A(x^2+2x+1)+B(x+1)+C)/(x+1)^3#
#color(white)(x^2/(x+1)^3) = (Ax^2+(2A+B)x+(A+B+C))/(x+1)^3#
Equating coefficients we have:
#{ (A=1), (2A+B=0), (A+B+C=0) :}#
Hence:
#{ (A=1), (B=-2), (C=1) :}#
So:
#x^2/(x+1)^3 = 1/(x+1)-2/(x+1)^2+1/(x+1)^3#
