How do you simplify #(3x-2)/(x+3)+7/(x^2-x-12)#?

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Answer 1 · 2017-07-02T11:31:02

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

First, factor out the denominator of the right hand term

#(3x-2)/(x+3)+7/((x+3)(x-4))#

Next multiply the numerator and denominator of the first term by #(x-4)# in order to get a common denominator.

#(x-4)/(x-4)(3x-2)/(x+3)+7/((x+3)(x-4))#

Combine the two fractions.

#((x-4)(3x-2)+7)/((x+3)(x-4))#

Expand the numerator

#(3x^2-12x-2x+8+7)/((x+3)(x-4))#

Simplify the numerator

#(3x^2-14x+15)/((x+3)(x-4))#

Factor the numerator

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