What is the answer to 1+1/x-1/(x^2)=0 ?

The answer to 1+1/x-1/(x^2)=0 is x=(-1+sqrt(5))/2 ,x=(-1-sqrt(5))/2

Solve for x: 1+1/x-1/(x^2)=0

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

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

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

Decimal Notation

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

Solution steps

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

Multiply by LCM

x^{2} + x - 1 = 0

Solve

x^{2} + x - 1 = 0 : 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}

x^{2} + \frac{x ^{2}}{( x + 1 ) ^{2}} = 3

6 = 9 - 90000 (\frac{1}{10000 + 3 t})

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

\frac{5}{x ^{2}} - \frac{54}{x} = 11

\frac{5}{x ^{2} - 9} - \frac{2}{x ^{2} - 4} = 0

What is the answer to 1+1/x-1/(x^2)=0 ?
The answer to 1+1/x-1/(x^2)=0 is x=(-1+sqrt(5))/2 ,x=(-1-sqrt(5))/2
Solve for x: 1+1/x-1/(x^2)=0
The solution is x=(-1+sqrt(5))/2 ,x=(-1-sqrt(5))/2