Limit

Problem: 

 

Solution:

The problem is not complete because we don't know where $x$ tends to, anyway we can still simplify.

$\begin{eqnarray*} & & \lim \frac{x^2 - 2x + 3}{2x^2 + 5x - 3} \\ &=& \lim \frac{x^2 - 2x + 3}{(2x - 1)(x + 3)} \end{eqnarray*}$ The numerator do not factor, so the problem is interesting really when $x \to 0.5$ or $x \to -3$, in both case it tends to infinity, otherwise just simply substitute the value.