How do you write the partial fraction decomposition of the rational expression #(3x^2 -7x+1) / (x-1)^3#?

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Answer 1 · 2016-11-21T06:36:52

The answer is #=(-3)/(x-1)^3-1/(x-1)^2+3/(x-1)#

The decomposition in partial fractions is

#(3x^2-7x+1)/(x-1)^3=A/(x-1)^3+B/(x-1)^2+C/(x-1)#

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

Therefore,

#(3x^2-7x+1)=A+B(x-1)+C(x-1)^2#

Let #x=1#, #=>#, #-3=A#

#A+B+C=1#

Coefficients of #x^2#
#3=C#

Coefficients of #x#

#-7=-B-2C#, #=>#, #B=-1#

so, #(3x^2-7x+1)/(x-1)^3=(-3)/(x-1)^3-1/(x-1)^2+3/(x-1)#