What is the answer to 9/x = 1/(3x)+1 ?

The answer to 9/x = 1/(3x)+1 is x= 26/3

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9/x = 1/(3x)+1

\frac{9}{x} = \frac{1}{3 x} + 1

x = \frac{26}{3}

Decimal Notation

x = 8.66666 \dots

Solution steps

\frac{9}{x} = \frac{1}{3 x} + 1

Multiply by LCM

27 = 1 + 3 x

Switch sides

1 + 3 x = 27

Move

1

to the right side

3 x = 26

Divide both sides by

3

x = \frac{26}{3}

Verify Solutions

Find undefined (singularity) points:

x = 0

Combine undefined points with solutions:

x = \frac{26}{3}

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

\frac{3}{x} - \frac{1}{3} = - 6

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

\frac{x}{8} = \frac{8}{x}

\frac{f}{5 n ^{3}} + h = g