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

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

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

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

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

Combine.

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

Apply the distributive property.

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

Simplify by cancelling.

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $4$ .

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{1}{2}$ into the numerator.

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

Factor $2$ out of $4$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply $2$ by $- 1$ .

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

Simplify the numerator.

Factor $2$ out of $2 x + 4 \cdot 1$ .

Factor $2$ out of $2 x$ .

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

Factor $2$ out of $4 \cdot 1$ .

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

Factor $2$ out of $2 (x) + 2 (2 \cdot 1)$ .

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

Multiply $2$ by $1$ .

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