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

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

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simplify 2/(sqrt(5)-1)

simplify

\frac{2}{5 - 1}

\frac{5 + 1}{2}

Decimal Notation

1.61803 \dots

Solution steps

\frac{2}{5 - 1}

Multiply by the conjugate

\frac{5 + 1}{5 + 1}

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

Expand

2 (5 + 1) : 25 + 2

Expand

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

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

Factor out common term

2 : 2 (5 + 1)

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

Factor the number:

4 = 2 \cdot 2

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

Cancel the common factor:

2

= \frac{5 + 1}{2}

x^{2} + 23 x = 0

\frac{m}{- 12} = 4

4 (5 x + 1) = \frac{1}{2} (20 x + 16) + 16

- 4 x^{2} - 8 x + 21 = 0

3 x^{3} + 18 x^{2} + 15 x