Answer
$\frac{2x^{2}-3}{(x+3)(x-3)(x-2)} ; x \ne -3,3,2;$
Work Step by Step
$\frac{x}{x^{2}-9} + \frac{x-1}{x^{2}-5x+6}$
Factors of $x^{2}-5x+6$ are $(x-3)(x-2)$
$x^{2}-9 = (x+3)(x-3) $ using the formula $a^{2}-b^{2} = (a+b)(a-b)$
$= \frac{x}{(x+3)(x-3)} + \frac{x-1}{(x-3)(x-2)} ; x \ne -3,3,2;$
Take LCD,
$= \frac{x(x-2)+(x-1)(x+3)}{(x+3)(x-3)(x-2)} ; x \ne -3,3,2;$
$= \frac{x^{2}-2x+x^{2}+3x-x-3}{(x+3)(x-3)(x-2)} ; x \ne -3,3,2;$
Combine like terms.
$=\frac{2x^{2}-3}{(x+3)(x-3)(x-2)} ; x \ne -3,3,2;$
