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

1 Answer
Jun 14, 2015

Answer:

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#.