What is (3+sqrt(8))/(2-2sqrt(8)) ?

The solution to (3+sqrt(8))/(2-2sqrt(8)) is -(11+8sqrt(2))/(14)

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simplify (3+sqrt(8))/(2-2sqrt(8))

simplify

\frac{3 + 8}{2 - 2 8}

- \frac{11 + 8 2}{14}

Decimal Notation

- 1.59383 \dots

Solution steps

\frac{3 + 8}{2 - 2 8}

Multiply by the conjugate

\frac{2 + 2 8}{2 + 2 8}

= \frac{( 3 + 8 ) ( 2 + 2 8 )}{( 2 - 2 8 ) ( 2 + 2 8 )}

Expand

(3 + 8) (2 + 28) : 22 + 162

Expand

(2 - 28) (2 + 28) : - 28

= \frac{22 + 16 2}{- 28}

Factor out common term

2 : 2 (11 + 82)

= \frac{2 ( 11 + 8 2 )}{- 28}

Factor the number:

28 = 2 \cdot 14

= \frac{2 ( 11 + 8 2 )}{- 2 \cdot 14}

Cancel the common factor:

2

= \frac{11 + 8 2}{- 14}

Apply the fraction rule:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{11 + 8 2}{14}

3 p \leq 15

x^{2} - 14 x + 24 = 0

5 + y = 9

n^{2} + 10 n + 7 = 0

What is (3+sqrt(8))/(2-2sqrt(8)) ?
The solution to (3+sqrt(8))/(2-2sqrt(8)) is -(11+8sqrt(2))/(14)