Question

$$\frac{(x-5)^{2}}{x^{2}-25}$$

Answer

(x-5)/(x+5)

Solution


Rewrite \({x}^{2}-25\) in the form \({a}^{2}-{b}^{2}\), where \(a=x\) and \(b=5\).
\[\frac{{(x-5)}^{2}}{{x}^{2}-{5}^{2}}\]
Use Difference of Squares: \({a}^{2}-{b}^{2}=(a+b)(a-b)\).
\[\frac{{(x-5)}^{2}}{(x+5)(x-5)}\]
Simplify.
\[\frac{x-5}{x+5}\]