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

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

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

simplify

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

2 - 3

Decimal

0.26794 \dots

Solution steps

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

Multiply by the conjugate

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

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

Expand

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

Expand

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

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

Factor out common term

4 : 4 (2 - 3)

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

Cancel the common factor:

4

= 2 - 3

24 x^{3} - 16 x^{2} + 8 x

\frac{9 x ^{2} y ^{7}}{3 x ^{2} y ^{7}}

- 5 \cdot (- 2)

(1 - 4 a x)^{2}

\frac{1 + \frac{1}{x}}{1 - \frac{1}{x ^{2}}}

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