Question 572396
(x-2)/(x^2+x-12)+x/(x^2-2x-3)={{{(x-2)/(x^2+x-12)+x/(x^2-2x-3)}}}=
I would factor denominators first and see what I can use for a common denominator.
{{{(x-2)/(x^2+x-12)+x/(x^2-2x-3)}}}={{{(x-2)/((x+4)(x-3))+x/((x-3)(x+1))}}} = {{{(x-2)(x+1)/((x+4)(x-3)(x+1))+x(x+4)/((x+4)(x-3)(x+1))}}}
Then I would work on the numerator parts leaving the denominators alone (and hoping to be able to simplify the result).
{{{(x-2)(x+1)/((x+4)(x-3)(x+1))+x(x+4)/((x+4)(x-3)(x+1))}}} = {{{(x^2-x-2)/((x+4)(x-3)(x+1))+(x^2+4x)/((x+4)(x-3)(x+1))}}} = {{{(2x^2+3x-2)/((x+4)(x-3)(x+1))}}}
We can factor the numerator
{{{(2x^2+3x-2)/((x+4)(x-3)(x+1))}}} = {{{(2x-1)(x+2)/((x+4)(x-3)(x+1))}}}
Nothing cancels out, so I'll call it fully simplified.