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\(Express $2 + \sqrt{2} + \frac{1}{2 + \sqrt{2}} + \frac{1}{\sqrt{2} - 2}$ in simplest form.\)

 Apr 20, 2019
 #2
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+2

Look at the last two fractions

 

The sum of these  =  [ √2 - 2] + [ √2 + 2 ]              2√2              2√2

                                 ________________   =    _____   =        ___  =   - √2 

                                      [ √2+ 2 ] [√2 - 2 ]            2 - 4               -2

 

So.....we just have

 

2 + √2  - √2  =

 

 2

 

cool cool cool            

 Apr 20, 2019

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