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

Feb 7, 2017

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

Explanation:

Let's factorise the numerator

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

So,

$y = \frac{{x}^{2} - 5 x + 6}{x - 3} = \frac{\cancel{x - 3} \left(x - 2\right)}{\cancel{x - 3}}$

$y = x - 2$

This is the equation of a line

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