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

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Answer 1 · 2016-12-01T16:35:50

#x=+-2 and y = 0#,

Expressed in partial fractions,

#y = g(x) = 3 +(5/2)/(x-2)+(3/2)/(x+2)#

This form readily discloses that

#x=+-2# represent the vertical asymptotes.

Also, as #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]}