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

The answer to x-1/x = 3/2 is x=2,x=-1/2

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x-1/x = 3/2

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

x = 2, x = - \frac{1}{2}

Decimal Notation

x = 2, x = - 0.5

Solution steps

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

Multiply by LCM

2 x^{2} - 2 = 3 x

Solve

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

x = 2, x = - \frac{1}{2}

Verify Solutions

Find undefined (singularity) points:

x = 0

Combine undefined points with solutions:

x = 2, x = - \frac{1}{2}

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

\frac{4}{9} = \frac{2}{x}

\frac{6 - x}{x} = 10

\frac{1}{x ^{2} + 1} = 0

\frac{2}{x} = 6