Simplify (2-2/(u+2))/(1/(u+2)+u/2)

$\frac{2 - \frac{2}{u + 2}}{\frac{1}{u + 2} + \frac{u}{2}}$

Multiply the numerator and denominator of the complex fraction by $(u + 2) \cdot 2$ .

Multiply $\frac{2 - \frac{2}{u + 2}}{\frac{1}{u + 2} + \frac{u}{2}}$ by $\frac{(u + 2) \cdot 2}{(u + 2) \cdot 2}$ .

$\frac{(u + 2) \cdot 2}{(u + 2) \cdot 2} \cdot \frac{2 - \frac{2}{u + 2}}{\frac{1}{u + 2} + \frac{u}{2}}$

Combine.

$\frac{(u + 2) \cdot 2 (2 - \frac{2}{u + 2})}{(u + 2) \cdot 2 (\frac{1}{u + 2} + \frac{u}{2})}$

Apply the distributive property.

$\frac{(u + 2) \cdot 2 \cdot 2 + (u + 2) \cdot 2 (- \frac{2}{u + 2})}{(u + 2) \cdot 2 \frac{1}{u + 2} + (u + 2) \cdot 2 \frac{u}{2}}$

Simplify by cancelling.

Cancel the common factor of $u + 2$ .

Move the leading negative in $- \frac{2}{u + 2}$ into the numerator.

$\frac{(u + 2) \cdot 2 \cdot 2 + (u + 2) \cdot 2 \frac{- 2}{u + 2}}{(u + 2) \cdot 2 \frac{1}{u + 2} + (u + 2) \cdot 2 \frac{u}{2}}$

Factor $u + 2$ out of $(u + 2) \cdot 2$ .

$\frac{(u + 2) \cdot 2 \cdot 2 + (u + 2) (2) \frac{- 2}{u + 2}}{(u + 2) \cdot 2 \frac{1}{u + 2} + (u + 2) \cdot 2 \frac{u}{2}}$

Cancel the common factor.

$\frac{(u + 2) \cdot 2 \cdot 2 + (u + 2) \cdot 2 \frac{- 2}{u + 2}}{(u + 2) \cdot 2 \frac{1}{u + 2} + (u + 2) \cdot 2 \frac{u}{2}}$

Rewrite the expression.

$\frac{(u + 2) \cdot 2 \cdot 2 + 2 \cdot - 2}{(u + 2) \cdot 2 \frac{1}{u + 2} + (u + 2) \cdot 2 \frac{u}{2}}$

Multiply $2$ by $- 2$ .

$\frac{(u + 2) \cdot 2 \cdot 2 - 4}{(u + 2) \cdot 2 \frac{1}{u + 2} + (u + 2) \cdot 2 \frac{u}{2}}$

Cancel the common factor of $u + 2$ .

Factor $u + 2$ out of $(u + 2) \cdot 2$ .

$\frac{(u + 2) \cdot 2 \cdot 2 - 4}{(u + 2) (2) \frac{1}{u + 2} + (u + 2) \cdot 2 \frac{u}{2}}$

Cancel the common factor.

$\frac{(u + 2) \cdot 2 \cdot 2 - 4}{(u + 2) \cdot 2 \frac{1}{u + 2} + (u + 2) \cdot 2 \frac{u}{2}}$

Rewrite the expression.

$\frac{(u + 2) \cdot 2 \cdot 2 - 4}{2 + (u + 2) \cdot 2 \frac{u}{2}}$

Cancel the common factor of $2$ .

Factor $2$ out of $(u + 2) \cdot 2$ .

$\frac{(u + 2) \cdot 2 \cdot 2 - 4}{2 + 2 \cdot (u + 2) \frac{u}{2}}$

Cancel the common factor.

$\frac{(u + 2) \cdot 2 \cdot 2 - 4}{2 + 2 \cdot (u + 2) \frac{u}{2}}$

Rewrite the expression.

$\frac{(u + 2) \cdot 2 \cdot 2 - 4}{2 + (u + 2) u}$

Simplify the numerator.

Apply the distributive property.

$\frac{(u \cdot 2 + 2 \cdot 2) \cdot 2 - 4}{2 + (u + 2) u}$

Move $2$ to the left of $u$ .

$\frac{(2 \cdot u + 2 \cdot 2) \cdot 2 - 4}{2 + (u + 2) u}$

Multiply $2$ by $2$ .

$\frac{(2 \cdot u + 4) \cdot 2 - 4}{2 + (u + 2) u}$

Apply the distributive property.

$\frac{2 u \cdot 2 + 4 \cdot 2 - 4}{2 + (u + 2) u}$

Multiply $2$ by $2$ .

$\frac{4 u + 4 \cdot 2 - 4}{2 + (u + 2) u}$

Multiply $4$ by $2$ .

$\frac{4 u + 8 - 4}{2 + (u + 2) u}$

Subtract $4$ from $8$ .

$\frac{4 u + 4}{2 + (u + 2) u}$

Factor $4$ out of $4 u + 4$ .

Factor $4$ out of $4 u$ .

$\frac{4 (u) + 4}{2 + (u + 2) u}$

Factor $4$ out of $4$ .

$\frac{4 (u) + 4 (1)}{2 + (u + 2) u}$

Factor $4$ out of $4 (u) + 4 (1)$ .

$\frac{4 (u + 1)}{2 + (u + 2) u}$

Simplify the denominator.

Apply the distributive property.

$\frac{4 (u + 1)}{2 + u \cdot u + 2 u}$

Multiply $u$ by $u$ .

$\frac{4 (u + 1)}{2 + u^{2} + 2 u}$

Reorder terms.

$\frac{4 (u + 1)}{u^{2} + 2 u + 2}$

Simplify (2-2/(u+2))/(1/(u+2)+u/2)

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