How do you find the Vertical, Horizontal, and Oblique Asymptote given $y = \frac{x^{2} - 5 x + 6}{x - 3}$ $y = (x^2 - 5x + 6)/( x - 3)$ ?

Question

1234 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-02-07T10:54:17

This is the equation of the line $y = x - 2$ $y=x-2$

Let's factorise the numerator

$x^{2} - 5 x + 6 = (x - 3) (x - 2)$ $x^2-5x+6=(x-3)(x-2)$

So,

$y=(x^2-5x+6)/(x-3)=(cancel(x-3)(x-2))/cancel(x-3)$

$y=x-2$

This is the equation of a line

graph{(x^2-5x+6)/(x-3) [-12.66, 12.65, -6.33, 6.33]}

How do you find the Vertical, Horizontal, and Oblique Asymptote given y = (x^2 - 5x + 6)/( x - 3)y=x2−5x+6x−3y = (x^2 - 5x + 6)/( x - 3)?