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

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

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| x/(x-1)|=2

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

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

Decimal Notation

x = 0.66666 \dots, x = 2

Solution steps

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

Simplify

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

\frac{∣ x ∣}{∣ x - 1 ∣} = 2

Multiply both sides by

∣ x - 1 ∣

∣ x ∣ = 2 ∣ x - 1 ∣

Solve

∣ x ∣ = 2 ∣ x - 1 ∣ : x = \frac{2}{3} or x = 2

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

Verify Solutions

Find undefined (singularity) points:

x = 1

Combine undefined points with solutions:

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

\frac{y + 7}{y} = \frac{2}{3}

n, \frac{m}{n p ^{2}} = k

\frac{2}{x} = 2

\frac{2}{x} = 3

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