Simplify 7/(5-u)-(2+u)/(5-u)

$\frac{7}{5 - u} - \frac{2 + u}{5 - u}$

Combine the numerators over the common denominator.

$\frac{7 - (2 + u)}{- u + 5}$

Simplify each term.

Apply the distributive property.

$\frac{7 - 1 \cdot 2 - u}{- u + 5}$

Multiply $- 1$ by $2$ .

$\frac{7 - 2 - u}{- u + 5}$

Reduce the expression by cancelling the common factors.

Subtract $2$ from $7$ .

$\frac{5 - u}{- u + 5}$

Cancel the common factor of $5 - u$ and $- u + 5$ .

Reorder terms.

$\frac{- u + 5}{- u + 5}$

Cancel the common factor.

$\frac{- u + 5}{- u + 5}$

Rewrite the expression.

$1$