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

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

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

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

x = \frac{2}{7}

Decimal Notation

x = 0.28571 \dots

Solution steps

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

Multiply by LCM

3 x^{2} + 2 (3 x - 1) = x (3 x - 1)

Expand

2 (3 x - 1) : 6 x - 2

3 x^{2} + 6 x - 2 = x (3 x - 1)

Expand

x (3 x - 1) : 3 x^{2} - x

3 x^{2} + 6 x - 2 = 3 x^{2} - x

Move

2

to the right side

3 x^{2} + 6 x = 3 x^{2} - x + 2

Subtract

3 x^{2} - x

from both sides

3 x^{2} + 6 x - (3 x^{2} - x) = 3 x^{2} - x + 2 - (3 x^{2} - x)

Simplify

7 x = 2

Divide both sides by

7

x = \frac{2}{7}

Verify Solutions

Find undefined (singularity) points:

x = \frac{1}{3}, x = 0

Combine undefined points with solutions:

x = \frac{2}{7}

c, p = \frac{x - c}{x + c}

\frac{1}{x} = - \frac{6}{3 x} + 5

\frac{3 x + 2}{x ^{2} + 7 x + 12} = 0

400 y^{- 4} - 41 y^{- 2} + 1 = 0

\frac{6}{9} = \frac{8}{x}

What is the answer to (3x)/(3x-1)+2/x =1 ?
The answer to (3x)/(3x-1)+2/x =1 is x= 2/7
Solve for x: (3x)/(3x-1)+2/x =1
The solution is x= 2/7