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

The answer to 1/(1-x)-1=2 is x= 2/3

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1/(1-x)-1=2

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

x = \frac{2}{3}

Decimal Notation

x = 0.66666 \dots

Solution steps

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

Move

1

to the right side

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

Multiply both sides by

1 - x

1 = 3 (1 - x)

Switch sides

3 (1 - x) = 1

Divide both sides by

3

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

Move

1

to the right side

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

Divide both sides by

- 1

x = \frac{2}{3}

Verify Solutions

Find undefined (singularity) points:

x = 1

Combine undefined points with solutions:

x = \frac{2}{3}

4 x^{2} - 16 x + 16 + \frac{4 x + 8}{x} = 0

\frac{x - 2}{5} = 1 - \frac{1}{2 x - 3}

x, y = \frac{x}{2 + x + 1}

\frac{x}{3 x - 5} = 2 x + 61 - 111 - 11

x, a = \frac{8 k + 2 p}{x}