+ is used in order to remove the square root, refer to the identity (a+b)(a-b) = a^2-b^2
Please tell me if my working for the following question is correct. Also, more importantly, I have some gaps in my math foundation, so please tell me what math topics I should revise/relearn for the questions I wrote in red. Thanks.
(I don't understand why + is used. Please tell me what topic I need to revise to fully understand this part)
(Why do I need to multiply this?)
Edit: The question should be I edited the original question above. Thanks TutorMeNate
Okay, now you have " " inside both roots where before you had " " in one of them.(Why do I need to multiply this?)
First, you change the sign because you are multiplying by the conjugate, which answers your initial question of what you should look up and review.
Second, and to be very blunt, you did a lot of pointless work. You're trying to find the limit as x approaches 4. Before you ever try to simplify a limit, always try to plug it in first. If it is undefined, then proceed to simplify. In this case, you get 0 when you plug in 4, meaning the answer is 0. You can also check this by using a graphing calculator.
I hope this helps!