What is (4+sqrt(2))/(2-sqrt(2)) ?

The solution to (4+sqrt(2))/(2-sqrt(2)) is 5+3sqrt(2)

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simplify (4+sqrt(2))/(2-sqrt(2))

simplify

\frac{4 + 2}{2 - 2}

5 + 32

Decimal Notation

9.24264 \dots

Solution steps

\frac{4 + 2}{2 - 2}

Multiply by the conjugate

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

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

Expand

(4 + 2) (2 + 2) : 10 + 62

Expand

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

= \frac{10 + 6 2}{2}

Factor out common term

2 : 2 (5 + 32)

= \frac{2 ( 5 + 3 2 )}{2}

Cancel the common factor:

2

= 5 + 32

(2 a - 5 b) (4 a^{2} + 10 ab + 25 b^{2})

(x - 2)^{2} + 9 (x - 2) + 4

2 x^{2} + 5 x^{2} - 4 x^{2} - x^{2}

(3 y + 4)^{2}

\frac{144}{180}

What is (4+sqrt(2))/(2-sqrt(2)) ?
The solution to (4+sqrt(2))/(2-sqrt(2)) is 5+3sqrt(2)