What is 2/(3+sqrt(5)) ?

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

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simplify 2/(3+sqrt(5))

simplify

\frac{2}{3 + 5}

\frac{3 - 5}{2}

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) : 6 - 25

Expand

(3 + 5) (3 - 5) : 4

= \frac{6 - 2 5}{4}

Factor out common term

2 : 2 (3 - 5)

= \frac{2 ( 3 - 5 )}{4}

Factor the number:

4 = 2 \cdot 2

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

Cancel the common factor:

2

= \frac{3 - 5}{2}

2 g - 13 = 3

∣ x - 9 ∣ = - 9

\frac{1}{3} + \frac{1}{15} + \frac{1}{35}

1 \geq \frac{m}{4} - 3

- 4 x^{2} - 11 x - 6 = 0