# What is the domain of (-3x^2)/(x^2+4x-45)?

Jun 19, 2015

The domain is all the real $x$ except:
$x = - 9$ and $x = 5$

#### Explanation:

In this division you must ensure to avoid a division by zero, i.e., to have a zero in the denominator.
The denominator is equal to zero when:
${x}^{2} + 4 x - 45 = 0$
This is a quadratic equation that you can solve, say, using the Quadratic Formula.
So:
${x}_{1 , 2} = \frac{- 4 \pm \sqrt{16 + 180}}{2} = \frac{- 4 \pm 14}{2} =$
so you have two values of $x$ that makes the denominator equal to zero:
${x}_{1} = \frac{- 4 + 14}{2} = 5$
${x}_{2} \frac{- 4 - 14}{2} = - 9$
These two values cannot be used by your function. All the other values of $x$ are allowed: