A function $f(x)$ is said to have a removable discontinuity at $x=a$ if both of the following conditions hold:

1. $f$ is either not defined or not continuous at $x=a$.

2. $f(a)$ could either be defined or redefined so that the new function is continuous at $x=a$.

Show that has a removable discontinuity at $x=0$ by

(a) verifying (1) in the definition above, and then

(b) verifying (2) in the definition above by determining a value of $f(0)$ that would make $f$ continuous at $x=0$.

$f(0)=$ would make $f$ continuous at $x=0$.

Hint: Try combining the fractions and simplifying.

The discontinuity at $x=2$ is actually not a removable discontinuity, just in case you were wondering.