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

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

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

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

x = \frac{1}{3}

Decimal Notation

x = 0.33333 \dots

Solution steps

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

Cross multiply

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

Move

1

to the right side

2 x^{2} - 3 x = 2 x^{2} - 1

Move

2 x^{2}

to the left side

- 3 x = - 1

Divide both sides by

- 3

x = \frac{1}{3}

Verify Solutions

Find undefined (singularity) points:

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

Combine undefined points with solutions:

x = \frac{1}{3}

y, v = y^{- 4}

- f (a) = \frac{6 x - 1}{5 x + 2}

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

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

(20) = (\frac{63 x}{63 + x})

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