Question about simplifying [2 - sqrt(6)] / [4 + sqrt(6)]

[cjcapta]

I am doing test corrections and my problem is: [2 - ?6] / [4 + ?6]. The directions say simplify.
My answer was [14 - 6?6] / 10 , which my teacher said was correct but I can simplify it further. The note on the paper says: simplify by 2.
At first I thought it made sense because 2 can go into 10 and 14 but then I realized that the 14 was connected to the 6?6 by subtraction not multiplication. Is there any other way to simplify this, or was my teacher incorrect and I had the right solution?

 

[galactus]

Re: Question about simplifying my answer on a test

You've got two fractions. Reduce them. 14/10=7/5, 6/10=3/5

Then, you have 5 in the denominator.

 

[Loren]

Re: Question about simplifying my answer on a test

[14 - 6?6] / 10 =

\(\displaystyle \frac{14 - 6\sqrt{6}}{10}=\frac{2(7-3\sqrt{6})}{10}=\frac{7-3\sqrt6}{5}\)

 

[cjcapta]

Thanks

Thank you very much