What is 2/(-2-5sqrt(2)) ?

The solution to 2/(-2-5sqrt(2)) is -(-2+5sqrt(2))/(23)

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simplify 2/(-2-5sqrt(2))

simplify

\frac{2}{- 2 - 5 2}

- \frac{- 2 + 5 2}{23}

Decimal Notation

- 0.22048 \dots

Solution steps

\frac{2}{- 2 - 5 2}

Multiply by the conjugate

\frac{- 2 + 5 2}{- 2 + 5 2}

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

Expand

2 (- 2 + 52) : - 4 + 102

Expand

(- 2 - 52) (- 2 + 52) : - 46

= \frac{- 4 + 10 2}{- 46}

Factor out common term

2 : 2 (- 2 + 52)

= \frac{2 ( - 2 + 5 2 )}{- 46}

Factor the number:

46 = 2 \cdot 23

= \frac{2 ( - 2 + 5 2 )}{- 2 \cdot 23}

Cancel the common factor:

2

= \frac{- 2 + 5 2}{- 23}

Apply the fraction rule:

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

= - \frac{- 2 + 5 2}{23}

(k x)^{2}

\frac{b ^{3} - a ^{3}}{3 ( b - a )}

(3 x - y)^{5}

x^{3} - 6 x + 9

x^{3} - 6 x + 5

What is 2/(-2-5sqrt(2)) ?
The solution to 2/(-2-5sqrt(2)) is -(-2+5sqrt(2))/(23)