What is the answer to (2x)/(x-1)-1/x =5 ?

The answer to (2x)/(x-1)-1/x =5 is x=-(-2+sqrt(7))/3 ,x=(2+sqrt(7))/3

Solve for x: (2x)/(x-1)-1/x =5

The solution is x=-(-2+sqrt(7))/3 ,x=(2+sqrt(7))/3

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

x = - \frac{- 2 + 7}{3}, x = \frac{2 + 7}{3}

Decimal Notation

x = - 0.21525 \dots, x = 1.54858 \dots

Solution steps

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

Multiply by LCM

2 x^{2} - (x - 1) = 5 x (x - 1)

Solve

2 x^{2} - (x - 1) = 5 x (x - 1) : x = - \frac{- 2 + 7}{3}, x = \frac{2 + 7}{3}

x = - \frac{- 2 + 7}{3}, x = \frac{2 + 7}{3}

Verify Solutions

Find undefined (singularity) points:

x = 1, x = 0

Combine undefined points with solutions:

x = - \frac{- 2 + 7}{3}, x = \frac{2 + 7}{3}

\frac{4}{y} = \frac{y - 6}{y - 4}

\frac{x ^{2} - 3 x - 4}{x + 2} = 0

r, M = \frac{N}{r}

\frac{150000 - 1000 P}{1000 P} = 0.4

(20) = (\frac{32.76 x}{32.76 + x})

What is the answer to (2x)/(x-1)-1/x =5 ?
The answer to (2x)/(x-1)-1/x =5 is x=-(-2+sqrt(7))/3 ,x=(2+sqrt(7))/3
Solve for x: (2x)/(x-1)-1/x =5
The solution is x=-(-2+sqrt(7))/3 ,x=(2+sqrt(7))/3