In this question, we apply limit concepts to get the desired limit, finding that the correct options are: A, D and E, leading to the result of the limit being
.
Limit:
The limit given is:

If we apply the usual thing, of just replacing x by 7, the denominator will be 0, so this is not possible.
When we have a term with roots, we rationalize it, multiplying both the denominator and the denominator by the conjugate.
Multiplication by the conjugate:
The term with the root is:

It's conjugate is:

Multiplying numerator and denominator by the conjugate, meaning option A is correct:

We do this because at the numerator we can apply:

Thus

Thus, we can simplify the factors of x - 7, meaning that option D is correct, and we get:

Now, we just calculate the limit:

Thus, option E is also correct.
Using a limit calculator, as given by the image below, we have that 1/6 is the correct answer.
For more on limits, you can check brainly.com/question/12207599