Rewrite \(81-{x}^{2}\) in the form \({a}^{2}-{b}^{2}\), where \(a=9\) and \(b=x\).
\[\frac{9}{9-x}-\frac{1}{{9}^{2}-{x}^{2}}\]
Use Difference of Squares: \({a}^{2}-{b}^{2}=(a+b)(a-b)\).
\[\frac{9}{9-x}-\frac{1}{(9+x)(9-x)}\]
Rewrite the expression with a common denominator.
\[\frac{9(9+x)-1}{(9-x)(9+x)}\]
Expand.
\[\frac{81+9x-1}{(9-x)(9+x)}\]
Simplify \(81+9x-1\) to \(9x+80\).
\[\frac{9x+80}{(9-x)(9+x)}\]
(9*x+80)/((9-x)*(9+x))
