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{- 3}{( x - 2 ) ^{2}} = 0

(x + x^{2} + x^{3}) + (\frac{1}{x} + \frac{1}{( x ^{2} )} + \frac{1}{( x ^{3} )}) = 28

270 = \frac{n}{2 [ 2 x ^{10} + ( n - 1 ) 5 ]}

\frac{7}{5 \cdot ( - 7 x ^{2} + 2 ) ^{2}} = \frac{5}{7}

\frac{2 x}{3 x + 6} = \frac{3}{2}

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