What is the answer to x/(x-2)=4 ?

The answer to x/(x-2)=4 is x= 8/3

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x/(x-2)=4

\frac{x}{x - 2} = 4

x = \frac{8}{3}

Decimal Notation

x = 2.66666 \dots

Solution steps

\frac{x}{x - 2} = 4

Multiply both sides by

x - 2

x = 4 (x - 2)

Expand

4 (x - 2) : 4 x - 8

x = 4 x - 8

Move

4 x

to the left side

- 3 x = - 8

Divide both sides by

- 3

x = \frac{8}{3}

Verify Solutions

Find undefined (singularity) points:

x = 2

Combine undefined points with solutions:

x = \frac{8}{3}

\frac{x}{x - 2} = 6

\frac{6}{4} = \frac{3}{x}

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

\frac{x + 7}{x + 3} = \frac{5}{x}

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