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

The answer to (3x-1)/(x+2)= 2/x is x=(3+sqrt(57))/6 ,x=(3-sqrt(57))/6

Solve for x: (3x-1)/(x+2)= 2/x

The solution is x=(3+sqrt(57))/6 ,x=(3-sqrt(57))/6

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

x = \frac{3 + 57}{6}, x = \frac{3 - 57}{6}

Solution steps

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

Cross multiply

(3 x - 1) x = (x + 2) \cdot 2

Solve

(3 x - 1) x = (x + 2) \cdot 2 : x = \frac{3 + 57}{6}, x = \frac{3 - 57}{6}

x = \frac{3 + 57}{6}, x = \frac{3 - 57}{6}

Verify Solutions

Find undefined (singularity) points:

x = - 2, x = 0

Combine undefined points with solutions:

x = \frac{3 + 57}{6}, x = \frac{3 - 57}{6}

\frac{9}{x} = - \frac{3}{10}

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

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

\frac{1}{5 m} = \frac{- 2}{3}

\frac{4}{x} + x = 5

What is the answer to (3x-1)/(x+2)= 2/x ?
The answer to (3x-1)/(x+2)= 2/x is x=(3+sqrt(57))/6 ,x=(3-sqrt(57))/6
Solve for x: (3x-1)/(x+2)= 2/x
The solution is x=(3+sqrt(57))/6 ,x=(3-sqrt(57))/6