What is (sqrt(3)-sqrt(6))/(sqrt(3)+\sqrt{6)} ?

The solution to (sqrt(3)-sqrt(6))/(sqrt(3)+\sqrt{6)} is -3+2sqrt(2)

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simplify (sqrt(3)-sqrt(6))/(sqrt(3)+\sqrt{6)}

simplify

\frac{3 - 6}{3 + 6}

- 3 + 22

Decimal Notation

- 0.17157 \dots

Solution steps

\frac{3 - 6}{3 + 6}

Multiply by the conjugate

\frac{3 - 6}{3 - 6}

= \frac{( 3 - 6 ) ( 3 - 6 )}{( 3 + 6 ) ( 3 - 6 )}

Expand

(3 - 6) (3 - 6) : 9 - 62

Expand

(3 + 6) (3 - 6) : - 3

= \frac{9 - 6 2}{- 3}

Factor out common term

3 : 3 (3 - 22)

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

Cancel the common factor:

3

= \frac{3 - 2 2}{- 1}

Apply the fraction rule:

\frac{a}{- 1} = - a

= - (3 - 22)

- (3 - 22) = - 3 + 22

= - 3 + 22

x^{2} = - 3

\frac{5 - x}{x - 6} \geq 0

- 1 r < - 2

ln (8 e)

x^{3} + 2 x^{2} - 5 x - 6

What is (sqrt(3)-sqrt(6))/(sqrt(3)+\sqrt{6)} ?
The solution to (sqrt(3)-sqrt(6))/(sqrt(3)+\sqrt{6)} is -3+2sqrt(2)