Answer
$\dfrac{4}{5}$
Work Step by Step
As we can see from the attached graph, as $x$ gets closer and closer to $1$ from the left and the right, the value of the function (the $y$-value) gets closer and closer to $\frac{4}{5}$. Thus the limit is
$\displaystyle \lim_{x\to1}\frac{x^3-x^2+3x-3}{x^2+3x-4}=\frac{4}{5}$
