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

The solution to (1+sqrt(5))/(1-sqrt(5)) is -(3+sqrt(5))/2

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simplify (1+sqrt(5))/(1-sqrt(5))

simplify

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

- \frac{3 + 5}{2}

Decimal Notation

- 2.61803 \dots

Solution steps

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

Multiply by the conjugate

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

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

Expand

(1 + 5) (1 + 5) : 6 + 25

Expand

(1 - 5) (1 + 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}

Apply the fraction rule:

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

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

2 x - 20

2^{1.25} - 1.2 5^{3}

\frac{1}{7} \times \frac{1}{7}

\frac{24 x ^{5} y ^{6}}{16 x ^{5} y ^{8}}

What is (1+sqrt(5))/(1-sqrt(5)) ?
The solution to (1+sqrt(5))/(1-sqrt(5)) is -(3+sqrt(5))/2