What is 2+sqrt(2)+1/(2+sqrt(2))+1/(sqrt(2)-2) ?

The solution to 2+sqrt(2)+1/(2+sqrt(2))+1/(sqrt(2)-2) is 2

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simplify 2+sqrt(2)+1/(2+sqrt(2))+1/(sqrt(2)-2)

simplify

2 + 2 + \frac{1}{2 + 2} + \frac{1}{2 - 2}

2

Solution steps

2 + 2 + \frac{1}{2 + 2} + \frac{1}{2 - 2}

Convert element to fraction:

2 = \frac{2}{1}

= \frac{2}{1} + 2 + \frac{1}{2 + 2} + \frac{1}{2 - 2}

Convert element to fraction:

2 = \frac{2}{1}

= \frac{2}{1} + \frac{2}{1} + \frac{1}{2 + 2} + \frac{1}{2 - 2}

\frac{2}{1} + \frac{2}{1} + \frac{1}{2 + 2} + \frac{1}{2 - 2} = \frac{- 4}{( 2 + 2 ) ( 2 - 2 )}

= \frac{- 4}{( 2 + 2 ) ( 2 - 2 )}

Apply Difference of Two Squares

(2 + 2) (2 - 2) : - 2

= \frac{- 4}{- 2}

Cancel

\frac{- 4}{- 2} : 2

= 2

\frac{5 x ^{2}}{4} \cdot \frac{6}{5}

268

\frac{\frac{x ^{2} + 9 x + 20}{x ^{2} - 25}}{\frac{x + 4}{x - 4}}

6 \frac{64 w ^{6}}{18 w ^{2} x ^{3}}

What is 2+sqrt(2)+1/(2+sqrt(2))+1/(sqrt(2)-2) ?
The solution to 2+sqrt(2)+1/(2+sqrt(2))+1/(sqrt(2)-2) is 2