How do you simplify #x/(x-3) - 3/(x+4) + 7/(x^2 + x - 12)#?

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Answer 1 · 2016-02-04T20:26:51

#(x^2+x+16)/(x^2+x-12)#

Given: #x/(x-3)-3/(x+4)+7/(x^2+x-12)# ...........................(1)

Observed that #(x-3)(x+4)=x^2+x-12#

Write equation 1 as:

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

#(x^2+4x-3x+9+7)/((x-3)(x+4))#

#(x^2+x+16)/((x-3)(x+4))#

or #(x^2+x+16)/(x^2+x-12)#