Answer:

Step-by-step explanation:
So first, we should always try direct substitution:

Plug -6 in for x:

This is the indeterminate form. This doesn't mean the limit does not exist, but rather we need to simplify it first.
Looking at the limit, we see that there is a square root in the numerator. Therefore, we can use the difference of two squares to cancel out the square root in the numerator. Recall the difference of two squares formula:

The expression in the numerator is:

Therefore, to cancel it out, we need to multiply by:

Essentially, you just change the sign. So, multiply both the numerator and denominator by this expression:

For the numerator, this is the difference of two squares pattern. Therefore:

The roots in the numerator cancel. 4 squared is 16. Simplify:

Simplify:

Factor out a negative 1 from the numerator:

The (x+6)s cancel out:

Now, plug -6 again:

Therefore:
