SOLUTION: Hello. Can someone tell me if I am correct? in words it is 2x minus the square root of seven divided by 2x plus the square root of seven. I got -------- -1 is this correct?

No it isn't.



You must multiply by .

It's legal to multiply by that because it just equals to 1. 

·

or:



Now FOIL out the numerator and denominator:



The two middle terms combine together in the 
top as 

The two middle terms  CANCEL OUT in the bottom.

So we have as the final answer:



Notice that in the original expression there were radicals in BOTH
the top AND the bottom.  In the final answer, the bottom contains NO
radicals.  That's the idea -- to rewrite as an expression with NO
radicals in the bottom.  The above method causes the radicals to
cancel out in the bottom.

Edwin