What is the answer to x-1/x = 8/3 ?

The answer to x-1/x = 8/3 is x=3,x=-1/3

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x-1/x = 8/3

x - \frac{1}{x} = \frac{8}{3}

x = 3, x = - \frac{1}{3}

Solution steps

x - \frac{1}{x} = \frac{8}{3}

Multiply by LCM

3 x^{2} - 3 = 8 x

Solve

3 x^{2} - 3 = 8 x : x = 3, x = - \frac{1}{3}

x = 3, x = - \frac{1}{3}

Verify Solutions

Find undefined (singularity) points:

x = 0

Combine undefined points with solutions:

x = 3, x = - \frac{1}{3}

\frac{8}{( x - 2 ) ^{3}} = 0

\frac{1}{x - 3} + 2 = \frac{9}{x - 3}

\frac{x}{4} = \frac{16}{x}

\frac{4}{x} = \frac{10}{7.5}

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