# How do you find the domain of the function f(x)= (2x+3)/(x^2+9x+20)?

Apr 16, 2015

Any value that makes the denominator $= 0$ is forbidden

So we need to know when ${x}^{2} + 9 x + 20 = 0$

If we factorise we get:
$\left(x + 4\right) \left(x + 5\right) = 0 \to x = - 4 \mathmr{and} x = - 5$

So these are not allowed. Any other $x$-value is.

Answer : $x \ne - 4 \mathmr{and} x \ne - 5$