# I get a solution of y=3 but how to solve for this limit?? lim(x->-4)(3x+12)/(x+4)

Apr 4, 2018

$3$

#### Explanation:

Substituting in $- 4$ right away yields

${\lim}_{x \to - 4} \frac{3 x + 12}{x + 4} = \frac{- 12 + 12}{- 4 + 4} = \frac{0}{0}$

This is an indeterminate form that tells us nothing, so we need to simplify.

${\lim}_{x \to - 4} 3 \frac{\cancel{x + 4}}{\cancel{x + 4}} = {\lim}_{x \to - 4} 3 = 3$

The limit is $3.$ What value of $x$ we're approaching doesn't impact the limit at all in this case, as all terms involving $x$ cancel out perfectly in our simplification.