Factor out the common term \(m\).
\[-\frac{2}{m(m-3)}+\frac{1}{{m}^{2}-9}\]
Rewrite \({m}^{2}-9\) in the form \({a}^{2}-{b}^{2}\), where \(a=m\) and \(b=3\).
\[-\frac{2}{m(m-3)}+\frac{1}{{m}^{2}-{3}^{2}}\]
Use Difference of Squares: \({a}^{2}-{b}^{2}=(a+b)(a-b)\).
\[-\frac{2}{m(m-3)}+\frac{1}{(m+3)(m-3)}\]
Rewrite the expression with a common denominator.
\[\frac{-2(m+3)+m}{m(m-3)(m+3)}\]
Expand.
\[\frac{-2m-6+m}{m(m-3)(m+3)}\]
Collect like terms.
\[\frac{(-2m+m)-6}{m(m-3)(m+3)}\]
Simplify \((-2m+m)-6\) to \(-m-6\).
\[\frac{-m-6}{m(m-3)(m+3)}\]
(-m-6)/(m*(m-3)*(m+3))
