Answer
Domain = $\mathbb{R}\backslash\{1/2\}$ or $\{x\in \mathbb{R}\ |\ x\neq 1/2\}$
Work Step by Step
The domain of a real function ( a function defined on real numbers)
is the set of numbers for which f(x) is defined.
$f(x)=\displaystyle \frac{x}{2x-1}$ can be calculated for any real number,
except for those yielding a zero in the denominator.
Here,
$2x-1=0$
$2x=1$
$x=1/2 \quad $must be excluded from the domain.
Domain = $\mathbb{R}\backslash\{1/2\}$ or $\{x\in \mathbb{R}\ |\ x\neq 1/2\}$