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

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

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simplify 1/(2-sqrt(5))

simplify

\frac{1}{2 - 5}

- 2 - 5

Decimal Notation

- 4.23606 \dots

Solution steps

\frac{1}{2 - 5}

Multiply by the conjugate

\frac{2 + 5}{2 + 5}

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

1 \cdot (2 + 5) = 2 + 5

(2 - 5) (2 + 5) = - 1

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

Apply the fraction rule:

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

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

Apply rule

\frac{a}{1} = a

= - (2 + 5)

Distribute parentheses

= - (2) - (5)

Apply minus-plus rules

+ (- a) = - a

= - 2 - 5

1 0^{5} \times 1 0^{3}

2.18 \cdot 1 0^{10}

- 1.2 + (- \frac{5}{3})

- 3 i - 72

\frac{1}{2} + \frac{4}{8}