What is the answer to | x/(x-3)|=1 ?

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

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| x/(x-3)|=1

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

x = \frac{3}{2}

Decimal Notation

x = 1.5

Solution steps

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

Simplify

\frac{x}{x - 3} : \frac{∣ x ∣}{∣ x - 3 ∣}

\frac{∣ x ∣}{∣ x - 3 ∣} = 1

Multiply both sides by

∣ x - 3 ∣

∣ x ∣ = ∣ x - 3 ∣

Solve

∣ x ∣ = ∣ x - 3 ∣ : x = \frac{3}{2}

x = \frac{3}{2}

Verify Solutions

Find undefined (singularity) points:

x = 3

Combine undefined points with solutions:

x = \frac{3}{2}

\frac{1}{x} + \frac{4}{x - 8} = 0

\frac{5}{1 - 3 x} = 2021

\frac{2 x + 8 b + 5 c}{x + b + c} = 5

\frac{6}{4} = \frac{9}{x}

\frac{x}{2 + 4 ( x + 2 )} = 14 - 2 x + 20