Simplify ((x^2)/4-x/2)/(1/2-x/4)

$\frac{\frac{x^{2}}{4} - \frac{x}{2}}{\frac{1}{2} - \frac{x}{4}}$

Step 1

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

Multiply $\frac{\frac{x^{2}}{4} - \frac{x}{2}}{\frac{1}{2} - \frac{x}{4}}$ by $\frac{4}{4}$ .

$\frac{4}{4} \cdot \frac{\frac{x^{2}}{4} - \frac{x}{2}}{\frac{1}{2} - \frac{x}{4}}$

Combine.

$\frac{4 (\frac{x^{2}}{4} - \frac{x}{2})}{4 (\frac{1}{2} - \frac{x}{4})}$

Step 2

Apply the distributive property.

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

Step 3

Simplify by cancelling.

Cancel the common factor of $4$ .

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $2$ .

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

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

Factor $2$ out of $4$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply $- 1$ by $2$ .

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

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{x}{4}$ into the numerator.

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 4

Simplify terms.

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

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

$\frac{x \cdot x - 2 x}{2 - x}$

Factor $x$ out of $- 2 x$ .

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

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

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

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

Factor $- 1$ out of $x$ .

$\frac{x (- 1 (- x) - 2)}{2 - x}$

Rewrite $- 2$ as $- 1 (2)$ .

$\frac{x (- 1 (- x) - 1 (2))}{2 - x}$

Factor $- 1$ out of $- 1 (- x) - 1 (2)$ .

$\frac{x (- 1 (- x + 2))}{2 - x}$

Reorder terms.

$\frac{x (- 1 (- x + 2))}{- x + 2}$

Cancel the common factor.

$\frac{x (- 1 (- x + 2))}{- x + 2}$

Divide $x \cdot (- 1)$ by $1$ .

$x \cdot (- 1)$

Simplify the expression.

Move $- 1$ to the left of $x$ .

$- 1 x$

Rewrite $- 1 x$ as $- x$ .

$- x$

Simplify ((x^2)/4-x/2)/(1/2-x/4)

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