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

The solution to (sqrt(5)+1)/(sqrt(5)-1) is (3+sqrt(5))/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify (sqrt(5)+1)/(sqrt(5)-1)

simplify

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

\frac{3 + 5}{2}

Decimal Notation

2.61803 \dots

Solution steps

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

Multiply by the conjugate

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

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

Expand

(5 + 1) (5 + 1) : 6 + 25

Expand

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

= \frac{6 + 2 5}{4}

Factor out common term

2 : 2 (3 + 5)

= \frac{2 ( 3 + 5 )}{4}

Factor the number:

4 = 2 \cdot 2

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

Cancel the common factor:

2

= \frac{3 + 5}{2}

\frac{3}{7} \div \frac{1}{2}

\frac{5}{7} \cdot 7

(- 10 x + 3) - (- 7 x^{2} + 5 x + 10)

4 \frac{1}{2} \cdot 2

∣ - 2 + 2 ∣

What is (sqrt(5)+1)/(sqrt(5)-1) ?
The solution to (sqrt(5)+1)/(sqrt(5)-1) is (3+sqrt(5))/2