What is (sqrt(2)-sqrt(6))/(sqrt(2)+\sqrt{6)} ?

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

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simplify (sqrt(2)-sqrt(6))/(sqrt(2)+\sqrt{6)}

simplify

\frac{2 - 6}{2 + 6}

- 2 + 3

Solution steps

\frac{2 - 6}{2 + 6}

Multiply by the conjugate

\frac{2 - 6}{2 - 6}

= \frac{( 2 - 6 ) ( 2 - 6 )}{( 2 + 6 ) ( 2 - 6 )}

Expand

(2 - 6) (2 - 6) : 8 - 43

Expand

(2 + 6) (2 - 6) : - 4

= \frac{8 - 4 3}{- 4}

Factor out common term

4 : 4 (2 - 3)

= \frac{4 ( 2 - 3 )}{- 4}

Cancel the common factor:

4

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

Apply the fraction rule:

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

= - (2 - 3)

- (2 - 3) = - 2 + 3

= - 2 + 3

z + (- z) = 4

∣ 2 (x - 1) + 12 ∣ \leq 10

5 x^{2} + 1 = 0

5 x < - 10

p^{2} - 169 q^{2}

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