How do you write the partial fraction decomposition of the rational expression #(x + 2) /( x(x - 4))#?

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Answer 1 · 2015-12-14T21:06:23

#(x+2)/(x(x-4))=3/(2(x-4))-1/(2x)#

#(x+2)/(x(x-4))=A/x+B/(x-4)#

#x+2=A(x-4)+Bx#

IF #x=0#:

#2=-4A#
#A=-1/2#

IF #x=4#:

#6=4B#
#B=3/2#

Therefore:

#(x+2)/(x(x-4))=3/(2(x-4))-1/(2x)#