Chapter P, Prerequisites - Section P.7 - Rational Expressions - P.7 Exercises - Page 51: 44

$\frac{x^{2}+3x+12}{(x-4)(x+6)}$

We form a common denominator: $\displaystyle \frac{x}{x-4}-\frac{3}{x+6}=\frac{x(x+6)}{(x-4)(x+6)}+\frac{-3(x-4)}{(x-4)(x+6)}=\frac{x^{2}+6x-3x+12}{(x-4)(x+6)}=\frac{x^{2}+3x+12}{(x-4)(x+6)}$