Question

How do you find the points of discontinuity of `y = ((x + 3)(x + 7)(x + 1)) /((x - 6)(x - 5))`?

Answer 1

This expression has discontinuities where the denominator is zero, which is when `x=5` and `x=6`.

Explanation:

Let `f(x) = ((x+3)(x+7)(x+1))/((x-6)(x-5))`

Both the numerator and the denominator are polynomials which in themselves are well behaved, continuous (infinitely differentiable) polynomials everywhere, but `f(x)` has severe discontinuities in the form of simple poles where the denominator is zero, which is when `x=5` and `x=6`.