Question

What are the points of discontinuity of `y =(x + 3)/((x - 4)(x + 3)`?

Answer 1

The function `f(x) = (x+3)/((x-4)(x+3))` is undefined at `x = -3` and at `x = 4`.

It is continuous on its domain. (Every rational function iscontinuous on its domain.)

Since `f` is defined near 4 and -3, there are discontinuities at 4 and -3.

(The discontinuity at 4 is infinite and that at -3 is removable.)

Answer 2

The discontinuity points are the zeroes of the denominator, so:

`x=4` and `x=-3`.