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

The answer to 2/(3x)= 3/x+1 is x=-7/3

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

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

x = - \frac{7}{3}

Decimal Notation

x = - 2.33333 \dots

Solution steps

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

Multiply by LCM

2 = 9 + 3 x

Switch sides

9 + 3 x = 2

Move

9

to the right side

3 x = - 7

Divide both sides by

3

x = - \frac{7}{3}

Verify Solutions

Find undefined (singularity) points:

x = 0

Combine undefined points with solutions:

x = - \frac{7}{3}

\frac{5}{9 x} = 1

8 - \frac{13}{x} = 4 + \frac{3}{x}

\frac{3}{x + 2} + 1 = 0

(x + 2) \cdot (\frac{80}{x - 2}) = 80

x, \frac{y}{x} = k