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

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

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simplify 1/(1+sqrt(5))

simplify

\frac{1}{1 + 5}

\frac{5 - 1}{4}

Decimal Notation

0.30901 \dots

Solution steps

\frac{1}{1 + 5}

Multiply by the conjugate

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

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

1 \cdot (1 - 5) = 1 - 5

(1 + 5) (1 - 5) = - 4

= \frac{1 - 5}{- 4}

Apply the fraction rule:

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

1 - 5 = - (5 - 1)

= \frac{5 - 1}{4}

1 - csc^{2} (x)

(7 x^{2}) (2 x^{3} + 5) (x^{2} - 4 x - 9)

\frac{17}{3} x + 17 - \frac{2}{3} x - 15

\frac{x ^{2} + x}{x ^{2}}

(37 + 5)^{2}