Question

What are the points of discontinuity? Are they all removable? Please show your work.

Answer 1

For this case we have the following expression:
 y = (x-5) / (x ^ 2 - 6x +5)
 Rewriting the expression we have:
 y = (x-5) / ((x-5) (x-1))
 Therefore, discontinuity points are those that make the denominator zero:
 x = 5
 x = 1
 The point of removable discontinuity is:
 x = 5
 Answer:
 Discontinuity:
 x = 5
 x = 1
 Removable:
 x = 5