Proving limit using the limit definition only Prove using the limit definition :
$$ \lim_{x \to 3} \frac{2x-5}{x^2-3x+4} = \frac{1}{4}  $$
When trying to prove it, i got to the expression:
$\frac{|x-8||x-3|}{|4(x^2-3x+4)|}$ 
But now i don't find a way to get rid of the denominator.
Can you help me?

Hint: 
$$x^2-3x+4=\left(x-\frac 32\right)^2 + \frac{7}{4}\geq 7/4$$
