What is the answer to 1/x+1/((x+1))=1 ?

The answer to 1/x+1/((x+1))=1 is x=(1+sqrt(5))/2 ,x=(1-sqrt(5))/2

Solve for x: 1/x+1/((x+1))=1

The solution is x=(1+sqrt(5))/2 ,x=(1-sqrt(5))/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

\frac{1}{x} + \frac{1}{( x + 1 )} = 1

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

Decimal Notation

x = 1.61803 \dots, x = - 0.61803 \dots

Solution steps

\frac{1}{x} + \frac{1}{( x + 1 )} = 1

Multiply by LCM

2 x + 1 = x (x + 1)

Solve

2 x + 1 = x (x + 1) : x = \frac{1 + 5}{2}, x = \frac{1 - 5}{2}

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

Verify Solutions

Find undefined (singularity) points:

x = 0, x = - 1

Combine undefined points with solutions:

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

9 x = \frac{1}{x}

\frac{6}{x} - 2 x = 9

\frac{7}{x} = \frac{4}{6}

\frac{9}{x + 2} - 1 = 0

(1 - 8000 r)^{- 1} = 1 + r (10000)

What is the answer to 1/x+1/((x+1))=1 ?
The answer to 1/x+1/((x+1))=1 is x=(1+sqrt(5))/2 ,x=(1-sqrt(5))/2
Solve for x: 1/x+1/((x+1))=1
The solution is x=(1+sqrt(5))/2 ,x=(1-sqrt(5))/2