Question

Question #c8dd3

Answer 1

Please see below.

Explanation:

`(x^2-15x)/(x^2+12)` is an expression, not an equation. It is called a rational expression because it is the ratio of two polynomials.

When we think of this expression as defining a function (of the kind called a 'rational function'),

`f(x) = (x^2-15x)/(x^2+12)`, then it makes sense to ask about continuity and discontinuities.

A rational function is continuous on its domain.

The domain of a rational function is the collection of all real numbers for which the denominator is NOT `0`.

To find the discontinuities, we find the places where the denominator IS `0`.

`x^2+12 = 0` at imaginary values `x = +-sqrt(-12)`.

Assuming that this question comes from a course in the calculus of real numbers, there are no discontinuities. (There are no real real numbers that make the denominator `0`.)