What is the answer to (6x-1)/(3x+2)=(2x)/(x-1) ?

The answer to (6x-1)/(3x+2)=(2x)/(x-1) is x= 1/11

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(6x-1)/(3x+2)=(2x)/(x-1)

\frac{6 x - 1}{3 x + 2} = \frac{2 x}{x - 1}

x = \frac{1}{11}

Decimal Notation

x = 0.09090 \dots

Solution steps

\frac{6 x - 1}{3 x + 2} = \frac{2 x}{x - 1}

Cross multiply

6 x^{2} - 7 x + 1 = 6 x^{2} + 4 x

Move

1

to the right side

6 x^{2} - 7 x = 6 x^{2} + 4 x - 1

Subtract

6 x^{2} + 4 x

from both sides

6 x^{2} - 7 x - (6 x^{2} + 4 x) = 6 x^{2} + 4 x - 1 - (6 x^{2} + 4 x)

Simplify

- 11 x = - 1

Divide both sides by

- 11

x = \frac{1}{11}

Verify Solutions

Find undefined (singularity) points:

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

Combine undefined points with solutions:

x = \frac{1}{11}

\frac{9}{4} - \frac{1}{2 x} = \frac{4}{x}

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

x - \frac{3 x + 5}{x + 2} = \frac{1}{x + 2}

\frac{1}{6} + \frac{1}{y} = \frac{1}{3}

\frac{7 - 3 x}{5 - x} - \frac{2 x}{3 - x} = 8

What is the answer to (6x-1)/(3x+2)=(2x)/(x-1) ?
The answer to (6x-1)/(3x+2)=(2x)/(x-1) is x= 1/11
Solve for x: (6x-1)/(3x+2)=(2x)/(x-1)
The solution is x= 1/11