Simplify (1/4-1/(8x))/(1/x-1/(2x^2))

$\frac{\frac{1}{4} - \frac{1}{8 x}}{\frac{1}{x} - \frac{1}{2 x^{2}}}$

Multiply the numerator and denominator of the complex fraction by $8 x^{2}$ .

Multiply $\frac{\frac{1}{4} - \frac{1}{8 x}}{\frac{1}{x} - \frac{1}{2 x^{2}}}$ by $\frac{8 x^{2}}{8 x^{2}}$ .

$\frac{8 x^{2}}{8 x^{2}} \cdot \frac{\frac{1}{4} - \frac{1}{8 x}}{\frac{1}{x} - \frac{1}{2 x^{2}}}$

Combine.

$\frac{8 x^{2} (\frac{1}{4} - \frac{1}{8 x})}{8 x^{2} (\frac{1}{x} - \frac{1}{2 x^{2}})}$

Apply the distributive property.

$\frac{8 x^{2} \frac{1}{4} + 8 x^{2} (- \frac{1}{8 x})}{8 x^{2} \frac{1}{x} + 8 x^{2} (- \frac{1}{2 x^{2}})}$

Simplify by cancelling.

Cancel the common factor of $4$ .

Factor $4$ out of $8 x^{2}$ .

$\frac{4 (2 x^{2}) \frac{1}{4} + 8 x^{2} (- \frac{1}{8 x})}{8 x^{2} \frac{1}{x} + 8 x^{2} (- \frac{1}{2 x^{2}})}$

Cancel the common factor.

$\frac{4 (2 x^{2}) \frac{1}{4} + 8 x^{2} (- \frac{1}{8 x})}{8 x^{2} \frac{1}{x} + 8 x^{2} (- \frac{1}{2 x^{2}})}$

Rewrite the expression.

$\frac{2 x^{2} + 8 x^{2} (- \frac{1}{8 x})}{8 x^{2} \frac{1}{x} + 8 x^{2} (- \frac{1}{2 x^{2}})}$

Cancel the common factor of $8 x$ .

Move the leading negative in $- \frac{1}{8 x}$ into the numerator.

$\frac{2 x^{2} + 8 x^{2} \frac{- 1}{8 x}}{8 x^{2} \frac{1}{x} + 8 x^{2} (- \frac{1}{2 x^{2}})}$

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

$\frac{2 x^{2} + 8 x (x) \frac{- 1}{8 x}}{8 x^{2} \frac{1}{x} + 8 x^{2} (- \frac{1}{2 x^{2}})}$

Cancel the common factor.

$\frac{2 x^{2} + 8 x \cdot x \frac{- 1}{8 x}}{8 x^{2} \frac{1}{x} + 8 x^{2} (- \frac{1}{2 x^{2}})}$

Rewrite the expression.

$\frac{2 x^{2} + x \cdot - 1}{8 x^{2} \frac{1}{x} + 8 x^{2} (- \frac{1}{2 x^{2}})}$

Cancel the common factor of $x$ .

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

$\frac{2 x^{2} + x \cdot - 1}{x (8 x) \frac{1}{x} + 8 x^{2} (- \frac{1}{2 x^{2}})}$

Cancel the common factor.

$\frac{2 x^{2} + x \cdot - 1}{x (8 x) \frac{1}{x} + 8 x^{2} (- \frac{1}{2 x^{2}})}$

Rewrite the expression.

$\frac{2 x^{2} + x \cdot - 1}{8 x + 8 x^{2} (- \frac{1}{2 x^{2}})}$

Cancel the common factor of $2 x^{2}$ .

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

$\frac{2 x^{2} + x \cdot - 1}{8 x + 8 x^{2} \frac{- 1}{2 x^{2}}}$

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

$\frac{2 x^{2} + x \cdot - 1}{8 x + 2 x^{2} (4) \frac{- 1}{2 x^{2}}}$

Cancel the common factor.

$\frac{2 x^{2} + x \cdot - 1}{8 x + 2 x^{2} \cdot 4 \frac{- 1}{2 x^{2}}}$

Rewrite the expression.

$\frac{2 x^{2} + x \cdot - 1}{8 x + 4 \cdot - 1}$

Multiply $4$ by $- 1$ .

$\frac{2 x^{2} + x \cdot - 1}{8 x - 4}$

Simplify terms.

Factor $x$ out of $2 x^{2} + x \cdot - 1$ .

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

$\frac{x (2 x) + x \cdot - 1}{8 x - 4}$

Factor $x$ out of $x \cdot - 1$ .

$\frac{x (2 x) + x (- 1)}{8 x - 4}$

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

$\frac{x (2 x - 1)}{8 x - 4}$

Factor $4$ out of $8 x - 4$ .

Factor $4$ out of $8 x$ .

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

Factor $4$ out of $- 4$ .

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

Factor $4$ out of $4 (2 x) + 4 (- 1)$ .

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

Cancel the common factor of $2 x - 1$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{x}{4}$

Simplify (1/4-1/(8x))/(1/x-1/(2x^2))

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