What is the answer to 2/(x-1)=3 ?

The answer to 2/(x-1)=3 is x= 5/3

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2/(x-1)=3

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

x = \frac{5}{3}

Decimal Notation

x = 1.66666 \dots

Solution steps

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

Multiply both sides by

x - 1

2 = 3 (x - 1)

Switch sides

3 (x - 1) = 2

Divide both sides by

3

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

Move

1

to the right side

x = \frac{5}{3}

Verify Solutions

Find undefined (singularity) points:

x = 1

Combine undefined points with solutions:

x = \frac{5}{3}

\frac{1}{x - 2} + 3 = \frac{13}{x - 2}

\frac{2}{5} + \frac{1}{x} = 4

\frac{7}{x} = \frac{4}{9}

\frac{3}{x ^{5}} = 27

x, y - \frac{1}{x ^{2}} = 0