How do you write the partial fraction decomposition of the rational expression #(x-5)/(x-2)^2#?

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Answer 1 · 2015-12-14T21:10:40

#(x-5)/(x-2)^2=1/(x-2)-3/(x-2)^2#

#(x-5)/(x-2)^2=A/(x-2)+B/(x-2)^2#

#x-5=A(x-2)+B#

#x-5=Ax-2A+B#

#x-5=x(A)+1(-2A+B)#

Thus, #{(A=1),(-2A+B=-5):}#

So, #{(A=1),(B=-3):}#

Plug back in:

#(x-5)/(x-2)^2=1/(x-2)-3/(x-2)^2#