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

The solution to (2+sqrt(2))/(2-sqrt(2)) is 3+2sqrt(2)

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

simplify

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

3 + 22

Solution steps

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

Multiply by the conjugate

\frac{2 + 2}{2 + 2}

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

Expand

(2 + 2) (2 + 2) : 6 + 42

Expand

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

= \frac{6 + 4 2}{2}

Factor out common term

2 : 2 (3 + 22)

= \frac{2 ( 3 + 2 2 )}{2}

Cancel the common factor:

2

= 3 + 22

4 \frac{1}{2} - 6

- (7.5 f + 3 g) - 4.4

\frac{5}{3} \div 7

16 x^{4} - 100 y^{4}

(4 x^{2} - 12 x - 10) - (2 x^{2} + x - 3)

What is (2+sqrt(2))/(2-sqrt(2)) ?
The solution to (2+sqrt(2))/(2-sqrt(2)) is 3+2sqrt(2)