What is (3+sqrt(5))/(1+sqrt(5)) ?

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

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simplify (3+sqrt(5))/(1+sqrt(5))

simplify

\frac{3 + 5}{1 + 5}

\frac{1 + 5}{2}

Solution steps

\frac{3 + 5}{1 + 5}

Multiply by the conjugate

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

= \frac{( 3 + 5 ) ( 1 - 5 )}{( 1 + 5 ) ( 1 - 5 )}

Expand

(3 + 5) (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}

Apply the fraction rule:

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

= \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}

e^{i} + e^{- i}

\frac{81}{5}

- 3 m + n - 5 n + (- 2)

y^{5} - 40 y^{3} + 144 y

39.2

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