Simplify \({5}^{2}\) to \(25\).
\[\frac{(x-5)(x+2)}{25-{x}^{2}}\]
Rewrite \(25-{x}^{2}\) in the form \({a}^{2}-{b}^{2}\), where \(a=5\) and \(b=x\).
\[\frac{(x-5)(x+2)}{{5}^{2}-{x}^{2}}\]
Use Difference of Squares: \({a}^{2}-{b}^{2}=(a+b)(a-b)\).
\[\frac{(x-5)(x+2)}{(5+x)(5-x)}\]
Factor out the negative sign in \(x-5\).
\[-\frac{(-x+5)(x+2)}{(5+x)(5-x)}\]
Regroup terms.
\[-\frac{(5-x)(x+2)}{(5+x)(5-x)}\]
Cancel \(5-x\).
\[-\frac{x+2}{5+x}\]
-(x+2)/(5+x)
