# How do you evaluate the limit (x^2-5x+4)/(x^2-2x-8) as x approaches 4?

Oct 27, 2016

Factor both the numerator and the denominator, to see what you can eliminate before substituting.

$= {\lim}_{x \to 4} \frac{\left(x - 4\right) \left(x - 1\right)}{\left(x - 4\right) \left(x + 2\right)}$

$= {\lim}_{x \to 4} \frac{x - 1}{x + 2}$

$= \frac{4 - 1}{4 + 2}$

$= \frac{3}{6}$

$= \frac{1}{2}$

Hopefully this helps!