# Hw do you find the domain for f(x)= (2x+7)/(x^2-13x-30)?

$f \left(x\right) = \frac{2 x + 7}{{x}^{2} - 13 x - 30}$
$f \left(x\right) = \frac{2 x + 7}{\left(x - 15\right) \left(x + 2\right)}$
which is defined for all values of $x$ for which the denominator is not $0$
that is for all values of $x$ except $x = 15$ and $x = - 2$
The Domain of $f \left(x\right)$
$= \mathbb{C} - \left\{- 2 , 15\right\}$
(replace $\mathbb{C}$ with $\mathbb{R}$ if you are restricted to Real numbers).