# Perpendicular Asymptotes

Algebra Level 3

$f(x)=\dfrac{x^2-6x+6}{2x-4}$ $g(x)=\dfrac{ax^2+bx+c}{x-d}$

You are given two functions $$f$$ and $$g$$ above, where $$a, b, c,$$ and $$d$$ are unknown constants. Also, you are given the following information about the function $$g$$:

• It has the same vertical asymptote as $$f$$.

• Its diagonal asymptote is perpendicular to that of $$f$$, and these two asymptotes intersect each other on the $$y$$-axis.

• The graphs of $$f$$ and $$g$$ have two intersection points. One of them is at $$x = -2$$. (In other words, $$f(-2) = g(-2)$$.)

What is the value of the other $$x$$-coordinate where $$f$$ and $$g$$ intersect?

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