#### Answer

$\displaystyle \frac{x-2}{x-3}$

#### Work Step by Step

To add rational expressions with the same denominator,
add numerators and place the sum over the common denominator.
If possible, factor and simplify the result.
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$\displaystyle \frac{x^{2}-4x}{x^{2}-x-6}+\frac{4x-4}{x^{2}-x-6} = \displaystyle \frac{x^{2}-4x+4x-4}{x^{2}-x-6}$
$= \displaystyle \frac{x^{2}-4}{x^{2}-x-6}$
... Numerator: a difference of squares,
... To factor the denominator, search for
... two factors of -6 whose sum is -1.
... We find +2 and -3
$= \displaystyle \frac{(x+2)(x-2)}{(x+2)(x-3)}\qquad$... reduce the common factors
$=\displaystyle \frac{x-2}{x-3} $