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

1 Answer
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+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: