What is the answer to 1/x = 2/x+1+1/(1-x) ?

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

Solve for x: 1/x = 2/x+1+1/(1-x)

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

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

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

Decimal Notation

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

Solution steps

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

Multiply by LCM

- x + 1 = 2 (- x + 1) + x (- x + 1) + x

Solve

- x + 1 = 2 (- x + 1) + x (- x + 1) + x : 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}

1 - \frac{3}{x} = - \frac{x}{x + 2}

x - \frac{7}{x + 8} = 2 x

- 3 - \frac{x}{x + 8} = \frac{8}{x + 8}

6 - \frac{2}{x ^{2}} = 0

\frac{- 10 x}{x ^{2} + 25} = 1

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