## Precalculus: Mathematics for Calculus, 7th Edition

$\frac{1}{4(x-2)}$
$=\frac{4x}{x^2-4}\times\frac{x+2}{16x}$ Multiply the two: $=\frac{4x(x+2)}{16x(x^2-4)}$ Cancel out the x-variable: $=\frac{4(x+2)}{16(x^2-4)}$ Factorise the $x^2-4$: $=\frac{4(x+2)}{16(x+2)(x-2)}$ Cancel out the $x+2$: $=\frac{4}{16(x-2)}$ Simplify the fraction: $=\frac{1}{4(x-2)}$