What is (2-sqrt(5))/(2+3sqrt(5)) ?

The solution to (2-sqrt(5))/(2+3sqrt(5)) is -(19-8sqrt(5))/(41)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify (2-sqrt(5))/(2+3sqrt(5))

simplify

\frac{2 - 5}{2 + 3 5}

- \frac{19 - 8 5}{41}

Decimal Notation

- 0.02710 \dots

Solution steps

\frac{2 - 5}{2 + 3 5}

Multiply by the conjugate

\frac{2 - 3 5}{2 - 3 5}

= \frac{( 2 - 5 ) ( 2 - 3 5 )}{( 2 + 3 5 ) ( 2 - 3 5 )}

Expand

(2 - 5) (2 - 35) : 19 - 85

Expand

(2 + 35) (2 - 35) : - 41

= \frac{19 - 8 5}{- 41}

Apply the fraction rule:

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

= - \frac{19 - 8 5}{41}

\frac{1}{x - 1} - 1

- 33 - 8 - 3

24 \cdot 8

412 - 275

What is (2-sqrt(5))/(2+3sqrt(5)) ?
The solution to (2-sqrt(5))/(2+3sqrt(5)) is -(19-8sqrt(5))/(41)