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

The answer to (2x)/(x-1)+5/(2x)=2 is x= 5/9

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(2x)/(x-1)+5/(2x)=2

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

x = \frac{5}{9}

Decimal Notation

x = 0.55555 \dots

Solution steps

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

Multiply by LCM

4 x^{2} + 5 (x - 1) = 4 x (x - 1)

Expand

5 (x - 1) : 5 x - 5

4 x^{2} + 5 x - 5 = 4 x (x - 1)

Expand

4 x (x - 1) : 4 x^{2} - 4 x

4 x^{2} + 5 x - 5 = 4 x^{2} - 4 x

Move

5

to the right side

4 x^{2} + 5 x = 4 x^{2} - 4 x + 5

Subtract

4 x^{2} - 4 x

from both sides

4 x^{2} + 5 x - (4 x^{2} - 4 x) = 4 x^{2} - 4 x + 5 - (4 x^{2} - 4 x)

Simplify

9 x = 5

Divide both sides by

9

x = \frac{5}{9}

Verify Solutions

Find undefined (singularity) points:

x = 1, x = 0

Combine undefined points with solutions:

x = \frac{5}{9}

\frac{2}{x - 1} + \frac{3}{x - 1} = 0

\frac{20 - 3 x}{x} = 2 x

4 = \frac{2}{3} - \frac{9}{x}

6 = \frac{49 - 1}{d - 7}

\frac{3}{x - 2} - \frac{7}{4 - x} = 0

What is the answer to (2x)/(x-1)+5/(2x)=2 ?
The answer to (2x)/(x-1)+5/(2x)=2 is x= 5/9
Solve for x: (2x)/(x-1)+5/(2x)=2
The solution is x= 5/9