Answer
$\frac{x^{2}+3x+12}{(x-4)(x+6)}$
Work Step by Step
$\frac{x}{x-4}-\frac{3}{x+6}$
Find the lowest common denominator (i.e. $(x-4)(x+6)$) and adjust the fractions:
$=\frac{x\times (x+6)}{(x-4)(x+6)}-\frac{3\times (x-4)}{(x-4)(x+6)}$
Expand any brackets:
$=\frac{x^{2}+6x}{(x-4)(x+6)}-\frac{3x-12}{(x-4)(x+6)}$
Combine the fractions:
$=\frac{x^{2}+6x-(3x-12)}{(x-4)(x+6)}$
Expand the negative sign:
$=\frac{x^{2}+6x-3x+12}{(x-4)(x+6)}$
Collect like terms:
$=\frac{x^{2}+3x+12}{(x-4)(x+6)}$
