How do you find the asymptotes for $g (x) = \frac{3 x^{2} + 2 x - 1}{x^{2} - 4}$ $g(x)=(3x^2+2x-1)/(x^2-4)$ ?

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Answer 1 · 2016-12-01T16:35:50

$x = \pm 2 and y = 0$ $x=+-2 and y = 0$ ,

Expressed in partial fractions,

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

This form readily discloses that

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

Also, as $x \to \pm \infty, y \to 0$ $x to +-oo, y to 0$ . 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]}

How do you find the asymptotes for g(x)=(3x^2+2x-1)/(x^2-4)g(x)=3x2+2x−1x2−4g(x)=(3x^2+2x-1)/(x^2-4)?