Rewrite \({m}^{2}-36\) in the form \({a}^{2}-{b}^{2}\), where \(a=m\) and \(b=6\).
\[\frac{7m-6}{{m}^{2}-{6}^{2}}-\frac{9}{m+6}\]
Use Difference of Squares: \({a}^{2}-{b}^{2}=(a+b)(a-b)\).
\[\frac{7m-6}{(m+6)(m-6)}-\frac{9}{m+6}\]
Rewrite the expression with a common denominator.
\[\frac{7m-6-9(m-6)}{(m+6)(m-6)}\]
Expand.
\[\frac{7m-6-9m+54}{(m+6)(m-6)}\]
Collect like terms.
\[\frac{(7m-9m)+(-6+54)}{(m+6)(m-6)}\]
Simplify \((7m-9m)+(-6+54)\) to \(-2m+48\).
\[\frac{-2m+48}{(m+6)(m-6)}\]
Factor out the common term \(2\).
\[\frac{-2(m-24)}{(m+6)(m-6)}\]
Move the negative sign to the left.
\[-\frac{2(m-24)}{(m+6)(m-6)}\]
-(2*(m-24))/((m+6)*(m-6))
