Answer
See below.
Work Step by Step
a) The domain is all the real numbers apart from the ones which make the fraction undefined, which is when the denominator is $0$, when $x-2=0\\x=2$
Thus the domain is all real numbers apart from $x=2$.
b) The x-intercepts are when $R(x)=0\\\frac{x(x-2)^2}{x-2}=0$
The fraction is $0$ when $x=0$ and $x=2$ but for the latter one the function is undefined, thus the only x-intercept is $x=0$.
