What is 2/(1+sqrt(5)) ?

The solution to 2/(1+sqrt(5)) is -(1-sqrt(5))/2

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simplify 2/(1+sqrt(5))

simplify

\frac{2}{1 + 5}

- \frac{1 - 5}{2}

Decimal Notation

0.61803 \dots

Solution steps

\frac{2}{1 + 5}

Multiply by the conjugate

\frac{1 - 5}{1 - 5}

= \frac{2 ( 1 - 5 )}{( 1 + 5 ) ( 1 - 5 )}

Expand

2 (1 - 5) : 2 - 25

Expand

(1 + 5) (1 - 5) : - 4

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

Factor out common term

2 : 2 (1 - 5)

= \frac{2 ( 1 - 5 )}{- 4}

Factor the number:

4 = 2 \cdot 2

= \frac{2 ( 1 - 5 )}{- 2 \cdot 2}

Cancel the common factor:

2

= \frac{1 - 5}{- 2}

Apply the fraction rule:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{1 - 5}{2}

\frac{v}{3} + 11 = 17

\frac{x}{3} - \frac{x}{5} = 7

12 x^{2} - 13 x + 3

10 x^{4} - 50 x^{3} - 7 x^{2} + 35 x

∣ 4 x + 7 ∣ < 21