# How do you find the asymptotes for g(x)=(3x^2+2x-1)/(x^2-4)?

Dec 1, 2016

$x = \pm 2 \mathmr{and} y = 0$,

#### Explanation:

Expressed in partial fractions,

$y = g \left(x\right) = 3 + \frac{\frac{5}{2}}{x - 2} + \frac{\frac{3}{2}}{x + 2}$

$x = \pm 2$ represent the vertical asymptotes.

Also, as $x \to \pm \infty , y \to 0$. And so, y = 0 represents the vertical

asymptote.

Illustrative graph is inserted.I

graph{y(x^2-4)-3x^2-2x+1=0 [-40, 40, -20, 20]}