# How do you find the asymptotes for y=(x-3)/(2x+5)?

Vertical Asymptote: $x = - \frac{5}{2}$
Horizontal Asymptote: $y = \frac{1}{2}$

#### Explanation:

For the vertical asymptote:

Equate the denominator to zero, then solve for x
$2 x + 5 = 0$
$2 x = - 5$
$x = - \frac{5}{2}$

For the horizontal asymptote:

Take the limit of the function

${\lim}_{x \rightarrow \infty} y = {\lim}_{x \rightarrow \infty} \frac{x - 3}{2 x + 5} = \frac{1}{2}$

and therefore

$y = \frac{1}{2}$ is a horizontal asymptote

graph{(y- (x-3)/(2x+5))(y-1/2)=0[-20,20,-10,10]}

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