Answer
$\dfrac{13}{28}\approx 0.46$
Work Step by Step
As we can see from the attached graph, as $x$ gets closer and closer to $3$ from the left and the right, the value of the function (the $y$-value) gets closer and closer to $\frac{13}{28}$. Thus the limit is
$\displaystyle \lim_{x\to3}\frac{x^3-3x^2+4x-12}{x^4-3x^3+x-3}=\frac{13}{28}\approx 0.46$
