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