What is the partial fraction decomposition of #f(x) = (-7x + 15)/(x^2 + 5x)#?

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Answer 1 · 2015-12-17T00:09:27

#(-7x+15)/(x^2+5x)=3/x-10/(x+5)#

Factor the denominator.

#(-7x+15)/(x(x+5))=A/x+B/(x+5)#

Multiply everything by #x(x+5)#.

#-7x+15=A(x+5)+Bx#

Plug in #0# for #x#:

#15=5A#
#A=3#

Plug in #-5# for #x#:

#50=-5B#
#B=-10#

Plug in these values.

#(-7x+15)/(x^2+5x)=3/x-10/(x+5)#