(4)

Case I) The function is

For a function to be continous, the denominator  of the function should not be zero.

x - 2 ≠ 0

x ≠ 2

Therefore is not continuous at x = 2.

Case II) The function is

Cancel the common terms

x - 2

For a function to be continous, the denominator  of the function should not be zero.

Therefore is continuous at x = 2.

Case III) The function is

For a function to be continuous, the denominator  of the function should not be zero.

Therefore is continous at x = 2.

Divide numerator and denominator by x

As then

Therefore