Answer
all real numbers apart from $3$ and $\frac{1}{4}$.
Work Step by Step
We know that for rational expressions the domain is all the real numbers, excluding when the denominator is $0$.
$4x^2-13x+3=4x^2-12x-x+3=4x(x-3)-(x-3)=(x-3)(4x-1)$
Here the denominator is $0$, when $x=3$ or $x=\frac{1}{4}$, thus the domain is all real numbers apart from $3$ and $\frac{1}{4}$.
