Question

How do I go about solving this? Do I make it into one big fraction or can I simplify the radical somehow?

Answer 1

Not sure how to find this limit algebraically.

However, you can evaluate it analytically.
Notice the domain is restricted to:
$x^2 \ \textgreater \ 4$
This means the right sided limit cannot exist.
You can only evaluate the left side limit.

As x-> -2 from the left. The first term goes to positive infinity and 2nd term goes to negative infinity.

$\infty - (-\infty) = \infty$

Therefore the limit is positive infinity.