## Precalculus: Mathematics for Calculus, 7th Edition

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