How do you find vertical, horizontal and oblique asymptotes for #(x^2+4x-2)/(x-2)#?

1 Answer
Dec 6, 2016

Answer:

Vertical: #uarr x = 2 darr #. Seldom realized oblique asymptote:
y = x+ 6. These are the asymptotes of the hyperbola represented by the equation. See illustrative graph.

Explanation:

Cross multiply and reorganize to the form

#x(y-x)-2y-4x+2=0#. This suggest the form

#(x+a)(y-x+b=c# and we have

#(x-2)(x-y+6)=-14# that represents the hyperbola with asymptotes

#x-2 = 0 and x-y+6=0#.

Now, look for the asymptotes in the graph.

graph{y(x-2)-x^2-4x+2=0 [-79.2, 79.2, -39.6, 39.6]}