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

The answer to 1/x-3= 1/(2x) is x= 1/6

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1/x-3= 1/(2x)

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

x = \frac{1}{6}

Decimal Notation

x = 0.16666 \dots

Solution steps

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

Multiply by LCM

2 - 6 x = 1

Move

2

to the right side

- 6 x = - 1

Divide both sides by

- 6

x = \frac{1}{6}

Verify Solutions

Find undefined (singularity) points:

x = 0

Combine undefined points with solutions:

x = \frac{1}{6}

2 x - 1 - \frac{1}{x} = 0

\frac{5}{x} + \frac{5}{2 x} = 6

\frac{3 x}{( x - 3 ) ( x - 4 )} = 2 x + 9

\frac{1}{( h + 6 )} (h + 6) = 1

\frac{10}{x} = 5