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

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

Solve for x: 1/x =x+1

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

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

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} = x + 1

Multiply both sides by

x

1 = x^{2} + x

Solve

1 = x^{2} + 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

Combine undefined points with solutions:

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

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

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

\frac{3}{4} = \frac{15}{x}

\frac{5}{x - 3} = \frac{7}{x - 9}

\frac{9}{x - 2} = 5 - \frac{6}{x - 2}

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