Simplify (2-(x^2)/2)/((x^2)/4+x/2)

$\frac{2 - \frac{x^{2}}{2}}{\frac{x^{2}}{4} + \frac{x}{2}}$

Multiply the numerator and denominator of the complex fraction by $4$ .

Multiply $\frac{2 - \frac{x^{2}}{2}}{\frac{x^{2}}{4} + \frac{x}{2}}$ by $\frac{4}{4}$ .

$\frac{4}{4} \cdot \frac{2 - \frac{x^{2}}{2}}{\frac{x^{2}}{4} + \frac{x}{2}}$

Combine.

$\frac{4 (2 - \frac{x^{2}}{2})}{4 (\frac{x^{2}}{4} + \frac{x}{2})}$

Apply the distributive property.

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

Simplify by cancelling.

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{x^{2}}{2}$ into the numerator.

$\frac{4 \cdot 2 + 4 \frac{- x^{2}}{2}}{4 \frac{x^{2}}{4} + 4 \frac{x}{2}}$

Factor $2$ out of $4$ .

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

Cancel the common factor.

$\frac{4 \cdot 2 + 2 \cdot 2 \frac{- x^{2}}{2}}{4 \frac{x^{2}}{4} + 4 \frac{x}{2}}$

Rewrite the expression.

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

Multiply $- 1$ by $2$ .

$\frac{4 \cdot 2 - 2 x^{2}}{4 \frac{x^{2}}{4} + 4 \frac{x}{2}}$

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 \cdot 2 - 2 x^{2}}{4 \frac{x^{2}}{4} + 4 \frac{x}{2}}$

Rewrite the expression.

$\frac{4 \cdot 2 - 2 x^{2}}{x^{2} + 4 \frac{x}{2}}$

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

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

Cancel the common factor.

$\frac{4 \cdot 2 - 2 x^{2}}{x^{2} + 2 \cdot 2 \frac{x}{2}}$

Rewrite the expression.

$\frac{4 \cdot 2 - 2 x^{2}}{x^{2} + 2 x}$

Simplify the numerator.

Multiply $4$ by $2$ .

$\frac{8 - 2 x^{2}}{x^{2} + 2 x}$

Rewrite $8 - 2 x^{2}$ in a factored form.

Factor $2$ out of $8 - 2 x^{2}$ .

Factor $2$ out of $8$ .

$\frac{2 (4) - 2 x^{2}}{x^{2} + 2 x}$

Factor $2$ out of $- 2 x^{2}$ .

$\frac{2 (4) + 2 (- x^{2})}{x^{2} + 2 x}$

Factor $2$ out of $2 (4) + 2 (- x^{2})$ .

$\frac{2 (4 - x^{2})}{x^{2} + 2 x}$

Rewrite $4$ as $2^{2}$ .

$\frac{2 (2^{2} - x^{2})}{x^{2} + 2 x}$

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 2$ and $b = x$ .

$\frac{2 (2 + x) (2 - x)}{x^{2} + 2 x}$

Simplify terms.

Factor $x$ out of $x^{2} + 2 x$ .

Factor $x$ out of $x^{2}$ .

$\frac{2 (2 + x) (2 - x)}{x \cdot x + 2 x}$

Factor $x$ out of $2 x$ .

$\frac{2 (2 + x) (2 - x)}{x \cdot x + x \cdot 2}$

Factor $x$ out of $x \cdot x + x \cdot 2$ .

$\frac{2 (2 + x) (2 - x)}{x (x + 2)}$

Cancel the common factor of $2 + x$ and $x + 2$ .

Reorder terms.

$\frac{2 (x + 2) (2 - x)}{x (x + 2)}$

Cancel the common factor.

$\frac{2 (x + 2) (2 - x)}{x (x + 2)}$

Rewrite the expression.

$\frac{2 (2 - x)}{x}$

Simplify (2-(x^2)/2)/((x^2)/4+x/2)

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