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

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

Cancel the common factor of $1$ and $- 1$ .

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

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

Move the negative in front of the fraction.

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

Combine $2$ and $\frac{1}{2 x}$ .

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

Reduce the expression $\frac{2}{2 x}$ by cancelling the common factors.

Cancel the common factor.

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

Rewrite the expression.

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

Multiply the numerator by the reciprocal of the denominator.

$- (1 x)$

Multiply $x$ by $1$ .

$- x$