# How do you find vertical, horizontal and oblique asymptotes for (x+3 )/ (x^2 + 8x + 15)?

Vertical Asymptotes:$x = - 5$
Horizontal Asymptote:$y = 0$
No Oblique Asymptote

#### Explanation:

To obtain the Horizontal Asymptote, take the limit of the function

${\lim}_{x \rightarrow \infty} y = {\lim}_{x \rightarrow \infty} \frac{x + 3}{{x}^{2} + 8 x + 15} = z e r o$

therefore, $y = 0$ is a Horizontal Asymptote

To obtain the Vertical Asymptote, equate the factors of the denominator to zero the solve for x.

$x + 5 = 0$

$x = - 5$

Kindly see the graph of $y = \frac{x + 3}{{x}^{2} + 8 x + 15}$ and the location of the imaginary asymptotes.

graph{y=(x+3)/(x^2+8x+15)[-20,20,-10,10]}

God bless....I hope the explanation is useful.