Question

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

Answer 1

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+4x-45=0`
This is a quadratic equation that you can solve, say, using the Quadratic Formula.
So:
`x_(1,2)=(-4+-sqrt(16+180))/2=(-4+-14)/2=`
so you have two values of `x` that makes the denominator equal to zero:
`x_1=(-4+14)/2=5`
`x_2(-4-14)/2=-9`
These two values cannot be used by your function. All the other values of `x` are allowed: