Evaluate: (2)/(m+1)-(m-1)/(m)

Expression: $\frac{ 2 }{ m+1 }-\frac{ m-1 }{ m }$

Write all numerators above the least common denominator $m \times \left( m+1 \right)$

$\frac{ 2m-\left( m+1 \right) \times \left( m-1 \right) }{ m \times \left( m+1 \right) }$

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

$\frac{ -{m}^{2}+2m+1 }{ {m}^{2}+m }$