What is 4/(1+sqrt(5)) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify 4/(1+sqrt(5))

simplify

\frac{4}{1 + 5}

- 1 + 5

Decimal Notation

1.23606 \dots

Solution steps

\frac{4}{1 + 5}

Multiply by the conjugate

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

= \frac{4 ( 1 - 5 )}{( 1 + 5 ) ( 1 - 5 )}

Expand

4 (1 - 5) : 4 - 45

Expand

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

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

Factor out common term

4 : 4 (1 - 5)

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

Cancel the common factor:

4

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

Apply the fraction rule:

\frac{a}{- 1} = - a

= - (1 - 5)

- (1 - 5) = - 1 + 5

= - 1 + 5

x^{2} - x y - 4 x + 4 y

- (x + 1)^{2} + (x + 1) + 1

b^{2} - 2 b c + c^{2}

(1 + 2 j) + (1 + 3 j)

\frac{5}{7} x (7 x - \frac{49}{50})