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

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

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

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

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

Cross multiply

1 - x = x^{2}

Solve

1 - x = x^{2} : 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}

\frac{4}{x} = - \frac{2}{17}

2 + \frac{2 x + 5}{x - 1} = - 3

\frac{5}{x} = - 6

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

2 (2 t + 4) = \frac{3}{4 ( 24 - 8 t )}

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