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

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

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

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

x = 2, x = - 1

Solution steps

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

Multiply by LCM

2 x - 2 (x - 1) = x (x - 1)

Solve

2 x - 2 (x - 1) = x (x - 1) : x = 2, x = - 1

x = 2, x = - 1

Verify Solutions

Find undefined (singularity) points:

x = 1

Combine undefined points with solutions:

x = 2, x = - 1

\frac{3}{x - 3} = 5 + \frac{x}{x - 3}

- \frac{1}{x} = 0

\frac{10}{x} = \frac{1}{2 x} + 38

\frac{39}{x} = - \frac{3}{29}

\frac{3}{5} = \frac{13}{x}