Evaluating limit directly -

If we try to evaluate the given limit directly then we get 0/0 which is an indeterminate form. Hence, we will have to first simplify the given function and then try evaluating limit again.

Simplifying the function -

To simplify the function we perform rationalization, we get:

Simplifying further, we get:

Evaluating limit again -

Now that we have removed the factor (x + 2) from numerator and denominator, we can try to evaluate limit again by considering the fact that x tends to -2, we get,

Answer: The value of the given limit is 1/2.