# How do you prove that the function f(x)=(x^2+7x+10)/(x+5)  is continuous everywhere but x=-5?

Nov 1, 2015

Factor and rewrite the function.

#### Explanation:

$f \left(x\right) = \frac{{x}^{2} + 7 x + 10}{x + 5}$

$= \frac{\left(x + 2\right) \left(x + 5\right)}{x + 5}$

$= x + 2$ for $x \ne - 5$

Use whatever tools you have developed to show that a linear function is continuous,

but note that $f \left(- 5\right)$ is not defined, so $f$ cannot be continuous at $- 5$.