# How do you find lim (x^2-x+4)/(3x^2+2x-3) as x->oo?

$\frac{1}{3}$
Divide numerator and the denominator by ${x}^{2}$. Accordingly, it is $\frac{1 - \frac{1}{x} + \frac{4}{x} ^ 2}{3 + \frac{2}{x} - \frac{3}{x} ^ 2}$. Now applying the limit $x \to \infty$, it becomes
= $\frac{1}{3}$