# How to find a horizontal asymptote (x^2 - 5x + 6)/( x - 3)?

Feb 29, 2016

There is no horizontal asymptote

#### Explanation:

There is no horizontal asymptote as degree of numerator $2$ is greater than that of denominator $1$ by one.

In such case, there is a possibility of a slant asymptote, but before concluding that let us factorize (x^2−5x+6) as follows:

(x^2−5x+6)=x^2-3x-2x+6=x(x-3)-2(x-3)=(x-2)(x-3)

Hence (x^2−5x+6)/(x−3) can be simplified as follows:

$\frac{\left(x - 2\right) \left(x - 3\right)}{x - 3}$ or

$\left(x - 2\right)$

Hence (x^2−5x+6)/(x−3) is the equation of just the line $y = \left(x - 2\right)$
(I do not think tis can be considered as slanting asymptote).

But as $x - 3$ appears in denominator the domain of$x$ in $y$ does not include $3$.