What is the answer to 1/(3x-1/3)=12 ?

The answer to 1/(3x-1/3)=12 is x= 5/36

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1/(3x-1/3)=12

\frac{1}{3 x - \frac{1}{3}} = 12

x = \frac{5}{36}

Decimal Notation

x = 0.13888 \dots

Solution steps

\frac{1}{3 x - \frac{1}{3}} = 12

Simplify

\frac{1}{3 x - \frac{1}{3}} : \frac{3}{9 x - 1}

\frac{3}{9 x - 1} = 12

Multiply both sides by

9 x - 1

3 = 12 (9 x - 1)

Switch sides

12 (9 x - 1) = 3

Divide both sides by

12

9 x - 1 = \frac{1}{4}

Move

1

to the right side

9 x = \frac{5}{4}

Divide both sides by

9

x = \frac{5}{36}

Verify Solutions

Find undefined (singularity) points:

x = \frac{1}{9}

Combine undefined points with solutions:

x = \frac{5}{36}

\frac{8}{3 x - 2} + \frac{6}{x + 1} = 2

x^{- 2} - 3 x^{- 1} + 2 = 0

0.08 = 1 - \frac{1127}{x}

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

\frac{20}{m} = 5