Answer
Domain: all the real numbers except $x=0$ and $x=\frac{1}{2}$
The zero:
$x=5$
Work Step by Step
$f(x)=\frac{x-5}{2x^2-x}$
Domain:
$2x^2-x\ne0$
$2x(x-\frac{1}{2})\ne0$
$x\ne0$ and $x\ne\frac{1}{2}$
The zeros:
$f(x)=0$
$\frac{x-5}{2x^2-x}=0$
$x-5=0$
$x=5$
