How do you write the partial fraction decomposition of the rational expression #7/(x^2-14x)#?

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Answer 1 · 2015-12-24T05:37:30

#7/(x^2-14x)=-1/(2x)+1/(2(x-14))#

Factor and then break up the denominator.

#7/(x(x-14))=A/x+B/(x-14)#

Find a common denominator of #x(x-14)#.

#7=A(x-14)+Bx#

Plug in #0# for #x#:

#7=-14A#
#A=-1/2#

Plug in #14# for #x#:

#7=14B#
#B=1/2#

Plug these values into the original expression.

#7/(x^2-14x)=-1/(2x)+1/(2(x-14))#