What is the answer to 1/x-x/6 = 2/3 ?

The answer to 1/x-x/6 = 2/3 is x=-2-sqrt(10),x=sqrt(10)-2

Solve for x: 1/x-x/6 = 2/3

The solution is x=-2-sqrt(10),x=sqrt(10)-2

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\frac{1}{x} - \frac{x}{6} = \frac{2}{3}

x = - 2 - 10, x = 10 - 2

Decimal

x = - 5.16227 \dots, x = 1.16227 \dots

Solution steps

\frac{1}{x} - \frac{x}{6} = \frac{2}{3}

Multiply by LCM

6 - x^{2} = 4 x

Solve

6 - x^{2} = 4 x : x = - 2 - 10, x = 10 - 2

x = - 2 - 10, x = 10 - 2

Verify Solutions

Find undefined (singularity) points:

x = 0

Combine undefined points with solutions:

x = - 2 - 10, x = 10 - 2

\frac{6 x - 7}{x + 7} - \frac{7}{6 x} = 6

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

\frac{4 x + 9}{x} = 12

- \frac{16}{5} = \frac{- 4}{1 - r}

\frac{6}{x + 8} = - \frac{3}{4}

What is the answer to 1/x-x/6 = 2/3 ?
The answer to 1/x-x/6 = 2/3 is x=-2-sqrt(10),x=sqrt(10)-2
Solve for x: 1/x-x/6 = 2/3
The solution is x=-2-sqrt(10),x=sqrt(10)-2