Rationalize the denominator of 2sqrt7/x+sqrt7

Question

I need steps to do this. Been a while since high school. Thanks

Answer 1

You have to remember that (a-b)(a+b) = a^2-b^2

You have a denominator of x+√7
So, if you multiply top and bottom by x-√7, you have

2√7 (x-√7)
---------------------
(x+√7)(x-√7)

2√7 x - 2√7√7
--------------------
(x)^2 - (√7)^2

2√7 x - 14
----------------
x^2-7