What is the answer to x/(2x-1)-1/x =0 ?

The answer to x/(2x-1)-1/x =0 is x=1

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x/(2x-1)-1/x =0

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

x = 1

Solution steps

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

Multiply by LCM

x^{2} - (2 x - 1) = 0

Solve

x^{2} - (2 x - 1) = 0 : x = 1

x = 1

Verify Solutions

Find undefined (singularity) points:

x = \frac{1}{2}, x = 0

Combine undefined points with solutions:

x = 1

a, ab - \frac{16}{ab} = 2

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

\frac{27}{x} + 7 = 10

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

\frac{1}{x} = \frac{5}{6}