Answer
$\displaystyle \left\{x\ |\ x \gt \frac{1}{2} \right\}$ or $\displaystyle \left(\frac{1}{2}, \ +\infty \right)$
Work Step by Step
$(2x-1)^{-1}=\displaystyle \frac{1}{2x-1}$
If this fraction is positive, then
its denominator is positive:
$ 2x-1 \gt 0\qquad$ ... add $+1$
$ 2x \gt 1\qquad$... multiply with $\displaystyle \frac{1}{2}$
$x \gt \displaystyle \frac{1}{2}$
Solution set: $\displaystyle \left\{x\ |\ x \gt \frac{1}{2} \right\}$ or $\displaystyle \left(\frac{1}{2}, \ +\infty \right)$
