What is the answer to 1/x = 4/(3x)+1 ?

The answer to 1/x = 4/(3x)+1 is x=-1/3

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1/x = 4/(3x)+1

\frac{1}{x} = \frac{4}{3 x} + 1

x = - \frac{1}{3}

Decimal Notation

x = - 0.33333 \dots

Solution steps

\frac{1}{x} = \frac{4}{3 x} + 1

Multiply by LCM

3 = 4 + 3 x

Switch sides

4 + 3 x = 3

Move

4

to the right side

3 x = - 1

Divide both sides by

3

x = - \frac{1}{3}

Verify Solutions

Find undefined (singularity) points:

x = 0

Combine undefined points with solutions:

x = - \frac{1}{3}

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

\frac{2}{x} = \frac{x}{32}

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

y, z = \frac{1}{y - g}

\frac{2 x - 1}{x + 2} = \frac{4}{5}