What are the removable and non-removable discontinuities, if any, of #f(x)=(x - 2) / (x^2 - 3x + 2 )#?

1 Answer
Jan 17, 2016

#x=2# is a removeable discontinuity and #x=1# is a non-removeable discontinuity.

Explanation:

factorizing the denominator we get

#f(x)=(x-2)/((x-2)(x-1))=(x-2)/(x-1)#.

#therefore x=2# is a removeable discontinuity since the factor #(x-2)# leading to division by zero cancelled out, and #x=1# is a non-removeable discontinuity since it leads to division by zero in the denominator.