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:

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

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