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

The answer to 1/x+2/3 =2x is x=(1+sqrt(19))/6 ,x=(1-sqrt(19))/6

Solve for x: 1/x+2/3 =2x

The solution is x=(1+sqrt(19))/6 ,x=(1-sqrt(19))/6

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

x = \frac{1 + 19}{6}, x = \frac{1 - 19}{6}

Decimal Notation

x = 0.89314 \dots, x = - 0.55981 \dots

Solution steps

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

Multiply by LCM

3 + 2 x = 6 x^{2}

Solve

3 + 2 x = 6 x^{2} : x = \frac{1 + 19}{6}, x = \frac{1 - 19}{6}

x = \frac{1 + 19}{6}, x = \frac{1 - 19}{6}

Verify Solutions

Find undefined (singularity) points:

x = 0

Combine undefined points with solutions:

x = \frac{1 + 19}{6}, x = \frac{1 - 19}{6}

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

\frac{1}{3 x - 2} + \frac{5}{x} = 0

(x) = \frac{1}{x}

- \frac{210}{( x + 10 ) ^{2}} = 0

\frac{x - 5}{6} = \frac{3}{x - 8}

What is the answer to 1/x+2/3 =2x ?
The answer to 1/x+2/3 =2x is x=(1+sqrt(19))/6 ,x=(1-sqrt(19))/6
Solve for x: 1/x+2/3 =2x
The solution is x=(1+sqrt(19))/6 ,x=(1-sqrt(19))/6