Factor out the common term \(m\).
\[(\frac{1}{m(m-1)}-\frac{1}{m-1})\times \frac{m}{m+2}+\frac{m+1}{m+2}\]
Rewrite the expression with a common denominator.
\[\frac{1-m}{m(m-1)}\times \frac{m}{m+2}+\frac{m+1}{m+2}\]
Factor out the negative sign in \(1-m\).
\[-\frac{-1+m}{m(m-1)}\times \frac{m}{m+2}+\frac{m+1}{m+2}\]
Regroup terms.
\[-\frac{m-1}{m(m-1)}\times \frac{m}{m+2}+\frac{m+1}{m+2}\]
Cancel \(m-1\).
\[-\frac{1}{m}\times \frac{m}{m+2}+\frac{m+1}{m+2}\]
Cancel \(m\).
\[-\frac{1}{m+2}+\frac{m+1}{m+2}\]
Regroup terms.
\[\frac{m+1}{m+2}-\frac{1}{m+2}\]
Join the denominators.
\[\frac{m+1-1}{m+2}\]
Simplify \(m+1-1\) to \(m\).
\[\frac{m}{m+2}\]
m/(m+2)
