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?

Algebra ->  Radicals -> 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?       Log On


   

Question 83381: 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? 2x-sq7 divided by 2x +sq7 Thanks
Answer by Edwin McCravy(20086) About Me  (Show Source):
You can put this solution on YOUR website!
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? 2x-sq7 divided by 2x +sq7 Thanks 

No it isn't.

%282x+-+sqrt%287%29%29%2F%282x+%2B+sqrt%287%29%29

You must multiply by %282x+-+sqrt%287%29%29%2F%282x+-+sqrt%287%29%29.

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

%282x+-+sqrt%287%29%29%2F%282x+%2B+sqrt%287%29%29·%282x+-+sqrt%287%29%29%2F%282x+-+sqrt%287%29%29

or:



Now FOIL out the numerator and denominator:



The two middle terms -2x%2Asqrt%287%29+-+2x%2Asqrt%287%29combine together in the 
top as -4x%2Asqrt%287%29

The two middle terms 2x%2Asqrt%287%29+-+2x%2Asqrt%287%29 CANCEL OUT in the bottom.

So we have as the final answer:

%284x%5E2+-+4x%2Asqrt%287%29+%2B+7%29%2F%284x%5E2+-+7%29

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