What is the answer to 4/x-1/3 = x/6 ?

The answer to 4/x-1/3 = x/6 is x=4,x=-6

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4/x-1/3 = x/6

\frac{4}{x} - \frac{1}{3} = \frac{x}{6}

x = 4, x = - 6

Solution steps

\frac{4}{x} - \frac{1}{3} = \frac{x}{6}

Multiply by LCM

24 - 2 x = x^{2}

Solve

24 - 2 x = x^{2} : x = 4, x = - 6

x = 4, x = - 6

Verify Solutions

Find undefined (singularity) points:

x = 0

Combine undefined points with solutions:

x = 4, x = - 6

\frac{3 x - 5}{x + 3} = \frac{3 x - 4}{2 x + 1}

x + \frac{30}{x} = 11

\frac{2}{x ^{3}} - \frac{1}{x ^{2}} = 0

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

\frac{9}{5} = \frac{10}{9 x}