Answer
$ \frac{3(x-2)}{(x-1)}$.
Work Step by Step
The given expression is
$\Rightarrow \frac{2x^2-8x-11}{x^2+3x-4}+\frac{x^2+14x-13}{x^2+3x-4}$
$\Rightarrow \frac{2x^2-8x-11+x^2+14x-13}{x^2+3x-4}$
Add like terms.
$\Rightarrow \frac{3x^2+6x-24}{x^2+3x-4}$
Factor out $3$ from the numerators.
$\Rightarrow \frac{3(x^2+2x-8)}{x^2+3x-4}$
Factor the numerator and the denominator as shown below.
$\Rightarrow x^2+2x-8$
Rewrite the middle term $2x$ as $4x-2x$.
$\Rightarrow x^2+4x-2x-8$
Group terms.
$\Rightarrow (x^2+4x)+(-2x-8)$
Factor each group.
$\Rightarrow x(x+4)-2(x+4)$
Factor out $(x+4)$.
$\Rightarrow (x+4)(x-2)$
$\Rightarrow x^2+3x-4$
Rewrite the middle term $2x$ as $4x-x$.
$\Rightarrow x^2+4x-x-4$
Group terms.
$\Rightarrow (x^2+4x)+(-x-4)$
Factor each group.
$\Rightarrow x(x+4)-1(x+4)$
Factor out $(x+4)$.
$\Rightarrow (x+4)(x-1)$
Back substitute all factors into the fraction.
$\Rightarrow \frac{3(x+4)(x-2)}{(x+4)(x-1)}$
Cancel common terms.
$\Rightarrow \frac{3(x-2)}{(x-1)}$.
