$\frac{ 2m-\left( m+1 \right) \times \left( m-1 \right) }{ m \times \left( m+1 \right) }$
Use $\left( a-b \right)\left( a+b \right)={a}^{2}-{b}^{2}$ to simplify the product$\frac{ 2m-\left( {m}^{2}-1 \right) }{ m \times \left( m+1 \right) }$
Distribute $m$ through the parentheses$\frac{ 2m-\left( {m}^{2}-1 \right) }{ {m}^{2}+m }$
When there is a $-$ in front of an expression in parentheses, change the sign of each term of the expression and remove the parentheses$\frac{ 2m-{m}^{2}+1 }{ {m}^{2}+m }$
Use the commutative property to reorder the terms$\frac{ -{m}^{2}+2m+1 }{ {m}^{2}+m }$