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

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

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

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

x = - 1

Solution steps

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

Simplify

\frac{1 - x}{x - 1} : - 1

- 1 = \frac{1}{x}

Multiply both sides by

x

- x = 1

Divide both sides by

- 1

x = - 1

Verify Solutions

Find undefined (singularity) points:

x = 1, x = 0

Combine undefined points with solutions:

x = - 1

\frac{3}{x} + \frac{1}{5 x} = 1

1 + 2 x = \frac{6}{x}

x^{- 2} + 5 x^{- 1} + 4 = 0

\frac{16}{x - 4} = \frac{4}{9}

\frac{1}{( 3 x - \frac{1}{3} )} = 12