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

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

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

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

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

Combine.

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

Apply the distributive property.

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

Simplify by cancelling.

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

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply $2$ by $2$ .

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

Cancel the common factor of $x$ .

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

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

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply $- 1$ by $2$ .

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

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

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply $2$ by $2$ .

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

Cancel the common factor of $2$ .

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

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

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Factor $2$ out of $4 - 2 x$ .

Factor $2$ out of $4$ .

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

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

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

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

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

Simplify the denominator.

Move $- 1$ to the left of $x^{2}$ .

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

Rewrite $- 1 x^{2}$ as $- x^{2}$ .

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

Rewrite $4 - x^{2}$ in a factored form.

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

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

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 $b = x$ .

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

Cancel the common factor of $2 - x$ .

Cancel the common factor.

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

Rewrite the expression.

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

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

Related Questions

Support LCMGCF.com by disabling your adblocker.