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

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

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

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

x = - 5

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

x = - 5

Verify Solutions

Find undefined (singularity) points:

x = - 1, x = 0

Combine undefined points with solutions:

x = - 5

\frac{4 x + 2}{x - 9} = \frac{3}{5}

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

\frac{9}{k - 7} = \frac{6}{k}

\frac{6}{x} = 3

\frac{1}{x - 1} + 5 = \frac{11}{x - 1}

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