## Precalculus: Mathematics for Calculus, 7th Edition

$\frac{(x-5)}{(x-4)}$
$=\frac{x^2-25}{x^2-16}\times\frac{x+4}{x+5}$ Multiply the two fractions: $=\frac{(x^2-25)(x+4)}{(x^2-16)(x+5)}$ Factorise $x^2-25$: $=\frac{(x-5)(x+5)(x+4)}{(x^2-16)(x+5)}$ Factorise $x^2-16$: $=\frac{(x-5)(x+5)(x+4)}{(x-4)(x+4)(x+5)}$ Simplify the fraction: $=\frac{(x-5)}{(x-4)}$