What is the answer to (x/((x-1)))^2+4(x/((x-1)))+2=0 ?

The answer to (x/((x-1)))^2+4(x/((x-1)))+2=0 is x=(4+sqrt(2))/7 ,x=(4-sqrt(2))/7

Solve for x: (x/((x-1)))^2+4(x/((x-1)))+2=0

The solution is x=(4+sqrt(2))/7 ,x=(4-sqrt(2))/7

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(\frac{x}{( x - 1 )})^{2} + 4 (\frac{x}{( x - 1 )}) + 2 = 0

x = \frac{4 + 2}{7}, x = \frac{4 - 2}{7}

Decimal Notation

x = 0.77345 \dots, x = 0.36939 \dots

Solution steps

(\frac{x}{( x - 1 )})^{2} + 4 (\frac{x}{( x - 1 )}) + 2 = 0

Multiply by LCM

x^{2} + 4 x (x - 1) + 2 (x - 1)^{2} = 0

Solve

x^{2} + 4 x (x - 1) + 2 (x - 1)^{2} = 0 : x = \frac{4 + 2}{7}, x = \frac{4 - 2}{7}

x = \frac{4 + 2}{7}, x = \frac{4 - 2}{7}

Verify Solutions

Find undefined (singularity) points:

x = 1

Combine undefined points with solutions:

x = \frac{4 + 2}{7}, x = \frac{4 - 2}{7}

\frac{( - \frac{4}{3} ) ^{- 2}}{x} = (\frac{8}{15})^{- 1}

x + \frac{3}{x} - 2 - 1 - \frac{x}{x} = \frac{41}{4}

\frac{3}{4 \cdot x ^{2} - 8 x + 3} = 0

2 (\frac{x ^{2} + 1}{x ^{2}}) + 5 (\frac{x + 1}{x}) + 1 = 0

\frac{( 2 x - 1 )}{3 + x} = \frac{( 2 x + 6 )}{5}

What is the answer to (x/((x-1)))^2+4(x/((x-1)))+2=0 ?
The answer to (x/((x-1)))^2+4(x/((x-1)))+2=0 is x=(4+sqrt(2))/7 ,x=(4-sqrt(2))/7
Solve for x: (x/((x-1)))^2+4(x/((x-1)))+2=0
The solution is x=(4+sqrt(2))/7 ,x=(4-sqrt(2))/7