How do you write the partial fraction decomposition of the rational expression # (2x-2)/((x-5)(x-3))#?

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Answer 1 · 2015-12-14T21:02:19

#4/(x-5)-2/(x-3)#

#(2x-2)/((x-5)(x-3))=A/(x-5)+B/(x-3)#

#2x-2=A(x-3)+B(x-5)#

IF #x=3#:

#2(3)-2=B(3-5)#
#B=-2#

IF #x=5#:

#2(5)-2=A(5-3)#
#A=4#

Thus,

#(2x-2)/((x-5)(x-3))=4/(x-5)-2/(x-3)#