Alg1.2.15

Express the following as a rational expression $\frac{[\frac{x^2-1}{x^2-25}]}{[\frac{x^2-4x-5}{x^2+4x-5}]}\,$ in its lowest terms.

Given expression is

$\frac{[\frac{x^2-1}{x^2-25}]}{[\frac{x^2-4x-5}{x^2+4x-5}]}\,$

Simplifying

$\frac{(x^2-1)(x^2+4x-5)}{(x^2-25)(x^2-4x-5)}\,$

$\frac{(x+1)(x-1)(x+5)(x-1)}{(x+5)(x-5)(x-5)(x+1)}\,$

$\frac{(x-1)(x-1)}{(x-5)(x-5)}\,$

$\frac{x^2-2x+1}{x^2-10x+25}\,$