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.