How do you write the partial fraction decomposition of the rational expression # (9x) / (x^2 + 2x - 8)#?

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Answer 1 · 2015-12-21T04:53:46

#6/(x+4)+3/(x-2)#

Factor the denominator.

#(9x)/((x+4)(x-2))=A/(x+4)+B/(x-2)#

Simplify.

#9x=A(x-2)+B(x+4)#

Plug in #-4# for #x#:

#9(-4)=A(-4-2)#
#A=6#

Plug in #2# for #x#:

#9(2)=B(2+4)#
#B=3#

Plug these values into the original statement.

#(9x)/(x^2+2x-8)=6/(x+4)+3/(x-2)#