# How do you find the domain of (x^2 – x – 6 )/(x^2 – 9x + 18 )?

Jun 16, 2016

$x \ne 3 \mathmr{and} x \ne 6$

#### Explanation:

You can find the domain by excluding that the denominator is null, that's

${x}^{2} - 9 x + 18 \ne 0$

or

$x \ne \frac{9 \pm \sqrt{{9}^{2} - 4 \cdot 18}}{2}$

$x \ne \frac{9 \pm \sqrt{81 - 72}}{2}$

$x \ne \frac{9 \pm \sqrt{9}}{2}$

$x \ne \frac{9 \pm 3}{2}$

$x \ne 3 \mathmr{and} x \ne 6$