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

The solution to (sqrt(5))/(1+sqrt(5)) is -(sqrt(5)-5)/4

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

simplify

\frac{5}{1 + 5}

- \frac{5 - 5}{4}

Solution steps

\frac{5}{1 + 5}

Multiply by the conjugate

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

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

Expand

5 (1 - 5) : 5 - 5

Expand

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

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

Apply the fraction rule:

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

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

12 + (- 9)

(3 x)^{- 4}

(8 - 6 i) - (4 - 4 i)

5 \frac{5}{8} \div 3 \frac{3}{4}

(4 x + 1) (2 x - 3)

What is (sqrt(5))/(1+sqrt(5)) ?
The solution to (sqrt(5))/(1+sqrt(5)) is -(sqrt(5)-5)/4