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

The solution to 3/(1-sqrt(5)) is -(3+3sqrt(5))/4

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify 3/(1-sqrt(5))

simplify

\frac{3}{1 - 5}

- \frac{3 + 3 5}{4}

Solution steps

\frac{3}{1 - 5}

Multiply by the conjugate

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

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

Expand

3 (1 + 5) : 3 + 35

Expand

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

= \frac{3 + 3 5}{- 4}

Apply the fraction rule:

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

= - \frac{3 + 3 5}{4}

\frac{3}{4} \cdot \frac{2}{7}

\frac{3}{4} - \frac{2}{6}

x^{2} + 6 x - 10 - 8 x^{2} - 3 x

(x^{3} - 2 x + 3) - (3 x^{2} + 4 x - 3)

2 x + 3 x^{- 1} - 5