What is 2/(sqrt(3)+\sqrt{5)} ?

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

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simplify 2/(sqrt(3)+\sqrt{5)}

simplify

\frac{2}{3 + 5}

- 3 + 5

Decimal Notation

0.50401 \dots

Solution steps

\frac{2}{3 + 5}

Multiply by the conjugate

\frac{3 - 5}{3 - 5}

= \frac{2 ( 3 - 5 )}{( 3 + 5 ) ( 3 - 5 )}

Expand

2 (3 - 5) : 23 - 25

Expand

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

= \frac{2 3 - 2 5}{- 2}

Factor out common term

2

= \frac{2 ( 3 - 5 )}{- 2}

Cancel the common factor:

2

= \frac{3 - 5}{- 1}

Apply the fraction rule:

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

= - (3 - 5)

- (3 - 5) = - 3 + 5

= - 3 + 5

24 x^{3} y^{4} - 18 x^{2} y^{5}

x^{2} + 12 x + 36 - 9 y^{2}

(- \frac{4}{5}) - \frac{7}{8}

3 x^{3} - 12 x^{2} - 9 x

16 + 2 \cdot 0.1

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