What is the answer to (2x}{x-1}-2=\frac{x-1)/x ?

The answer to (2x}{x-1}-2=\frac{x-1)/x is x=2+sqrt(3),x=2-sqrt(3)

Solve for x: (2x}{x-1}-2=\frac{x-1)/x

The solution is x=2+sqrt(3),x=2-sqrt(3)

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

x = 2 + 3, x = 2 - 3

Decimal Notation

x = 3.73205 \dots, x = 0.26794 \dots

Solution steps

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

Multiply by LCM

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

Solve

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

x = 2 + 3, x = 2 - 3

Verify Solutions

Find undefined (singularity) points:

x = 1, x = 0

Combine undefined points with solutions:

x = 2 + 3, x = 2 - 3

28 x - 33 = \frac{28}{x}

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

2 = \frac{9}{s - 5}

- 8 + \frac{4 x}{x + 1} = - 6 x

\frac{3}{4} = \frac{12}{x}

What is the answer to (2x}{x-1}-2=\frac{x-1)/x ?
The answer to (2x}{x-1}-2=\frac{x-1)/x is x=2+sqrt(3),x=2-sqrt(3)
Solve for x: (2x}{x-1}-2=\frac{x-1)/x
The solution is x=2+sqrt(3),x=2-sqrt(3)