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

The answer to x/(x-2)-(x-2)/x = 5/2 is x=(9+sqrt(41))/5 ,x=(9-sqrt(41))/5

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

The solution is x=(9+sqrt(41))/5 ,x=(9-sqrt(41))/5

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

x = \frac{9 + 41}{5}, x = \frac{9 - 41}{5}

Decimal Notation

x = 3.08062 \dots, x = 0.51937 \dots

Solution steps

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

Multiply by LCM

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

Solve

2 x^{2} - 2 (x - 2)^{2} = 5 x (x - 2) : x = \frac{9 + 41}{5}, x = \frac{9 - 41}{5}

x = \frac{9 + 41}{5}, x = \frac{9 - 41}{5}

Verify Solutions

Find undefined (singularity) points:

x = 2, x = 0

Combine undefined points with solutions:

x = \frac{9 + 41}{5}, x = \frac{9 - 41}{5}

\frac{1}{x + 7} + \frac{1}{x - 3} = 0

\frac{6}{x - 14} = \frac{8}{2}

- \frac{7}{x - 1} + 4 x = - \frac{7 x}{x - 1}

\frac{7}{15} = \frac{42}{n}

\frac{1}{x + 4} + \frac{8}{x ^{2} - 16} = 1

What is the answer to x/(x-2)-(x-2)/x = 5/2 ?
The answer to x/(x-2)-(x-2)/x = 5/2 is x=(9+sqrt(41))/5 ,x=(9-sqrt(41))/5
Solve for x: x/(x-2)-(x-2)/x = 5/2
The solution is x=(9+sqrt(41))/5 ,x=(9-sqrt(41))/5