What is (sqrt(2)-sqrt(5))/(sqrt(2)+\sqrt{5)} ?

The solution to (sqrt(2)-sqrt(5))/(sqrt(2)+\sqrt{5)} is -(7-2sqrt(10))/3

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simplify (sqrt(2)-sqrt(5))/(sqrt(2)+\sqrt{5)}

simplify

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

- \frac{7 - 2 10}{3}

Solution steps

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

Multiply by the conjugate

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

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

Expand

(2 - 5) (2 - 5) : 7 - 210

Expand

(2 + 5) (2 - 5) : - 3

= \frac{7 - 2 10}{- 3}

Apply the fraction rule:

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

= - \frac{7 - 2 10}{3}

- 3 (z + 4)^{2} = - 108

\frac{9 ^{n}}{3 ^{2 n + 1}}

\frac{x}{3} > 4

(2^{- 4})^{- 3}

u^{2} + 3 u - 28 = 0

What is (sqrt(2)-sqrt(5))/(sqrt(2)+\sqrt{5)} ?
The solution to (sqrt(2)-sqrt(5))/(sqrt(2)+\sqrt{5)} is -(7-2sqrt(10))/3