What is (sqrt(2)+sqrt(6))/(sqrt(6)+\sqrt{8)} ?

The solution to (sqrt(2)+sqrt(6))/(sqrt(6)+\sqrt{8)} is sqrt(3)-1

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simplify (sqrt(2)+sqrt(6))/(sqrt(6)+\sqrt{8)}

simplify

\frac{2 + 6}{6 + 8}

3 - 1

Decimal Notation

0.73205 \dots

Solution steps

\frac{2 + 6}{6 + 8}

Multiply by the conjugate

\frac{6 - 8}{6 - 8}

= \frac{( 2 + 6 ) ( 6 - 8 )}{( 6 + 8 ) ( 6 - 8 )}

Expand

(2 + 6) (6 - 8) : - 23 + 2

Expand

(6 + 8) (6 - 8) : - 2

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

Factor out common term

2 : 2 (- 3 + 1)

= \frac{2 ( - 3 + 1 )}{- 2}

Cancel the common factor:

2

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

Apply the fraction rule:

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

= - (- 3 + 1)

- (- 3 + 1) = 3 - 1

= 3 - 1

\frac{\frac{\frac{5}{2}}{\frac{4}{1}}}{2}

4 a^{2} - 9 b^{6}

\frac{60 a ^{2} b ^{3}}{24 c}

\frac{2}{3} \div \frac{1}{12}

x (y - z) - w (y - z)

What is (sqrt(2)+sqrt(6))/(sqrt(6)+\sqrt{8)} ?
The solution to (sqrt(2)+sqrt(6))/(sqrt(6)+\sqrt{8)} is sqrt(3)-1