Question 132237
The domain is the value(s) that we can replace x with safely.

Your function is

15/(x^2 - 400)

Your denominator is clearly the difference of two perfect squares.

Your denominator becomes the following two factors: (x - 20) (x + 20).

We set each factor to = 0 and solve for x.

x - 20 = 0

x = 20

==========

x + 20 = 0

x = -20

What is the domain?

The domain will be ALL REAL NUMBERS EXCEPT x = -20 and x = 20?

WHY?

If you replace x with -20 and 20 in the original function, you get a ZERO in the denominator of your fraction.  Division by ZERO is NOT allowed in the world of math.

That is the reason why x CANNOT be -20 or 20 for this function.

Final answer:  The domain is ALL REAL NUMBERS EXCEPT x = -20 and x = 20?