# What are the asymptotes of (x^2+4)/(6x-5x^2)?

Jul 14, 2018

Vertical asymptotes are $x = 0 , x = \frac{6}{5}$ and the horizontal asymptote is $y = - \frac{1}{5}$

#### Explanation:

writing your term in the form

$\frac{{x}^{2} + 4}{x \left(6 - 5 x\right)}$ so we get the Asymptote when the denominator is equal to Zero:

This is $x = 0$ or $x = \frac{6}{5}$
no we compute the Limit for $x$ tends to $\infty$

writing

$\frac{{x}^{2} \left(1 + \frac{4}{x} ^ 2\right)}{{x}^{2} \left(\frac{6}{x} - 5\right)}$ and this tends to $- \frac{1}{5}$ for $x$ tends to infinity.