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

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

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

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

x = \frac{5}{2}

Decimal Notation

x = 2.5

Solution steps

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

Multiply by LCM

1 = 6 - 2 x

Switch sides

6 - 2 x = 1

Move

6

to the right side

- 2 x = - 5

Divide both sides by

- 2

x = \frac{5}{2}

Verify Solutions

Find undefined (singularity) points:

x = 0

Combine undefined points with solutions:

x = \frac{5}{2}

\frac{x}{x - 2} = 8

10 = \frac{50}{x}

\frac{7}{3 w} + \frac{9}{w} = 1

2 x - \frac{16}{x} = 4

\frac{34}{x} = \frac{- 17}{2}