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

This expression has discontinuities where the denominator is zero, which is when $x = 5$ and $x = 6$.
Let $f \left(x\right) = \frac{\left(x + 3\right) \left(x + 7\right) \left(x + 1\right)}{\left(x - 6\right) \left(x - 5\right)}$
Both the numerator and the denominator are polynomials which in themselves are well behaved, continuous (infinitely differentiable) polynomials everywhere, but $f \left(x\right)$ has severe discontinuities in the form of simple poles where the denominator is zero, which is when $x = 5$ and $x = 6$.