# How do you find the asymptotes for [(3x^2) + 14x + 4] / [x+2]?

Mar 3, 2016

One vertical asymptote $x + 2 = 0$ and one slanting asymptote given by $y = 3 x$.

#### Explanation:

To find the asymptotes of $\frac{3 {x}^{2} + 14 x + 4}{x + 2}$

we first observe the denominator $\left(x + 2\right)$, which shows that the function has one vertical asymptote $x + 2 = 0$.

Further, highest degree of numerator is two and that of denominator is one, and their ratio is $3 {x}^{2} / x = 3 x$.

Hence, we have a slanting asymptote given by $y = 3 x$

graph{(3x^2+14x+4)/(x+2) [-10, 10, -5, 5]}