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

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

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

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

x = - 5

Solution steps

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

Multiply by LCM

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

Expand

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

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

Expand

- 5 (x + 1) : - 5 x - 5

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

Add similar elements:

4 x - 5 x = - x

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

Subtract

4 x^{2} - x

from both sides

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

Simplify

x = - 5

Verify Solutions

Find undefined (singularity) points:

x = - 1, x = 0

Combine undefined points with solutions:

x = - 5

\frac{8}{7} = \frac{4}{x}

j, a = \frac{j + b}{j - c}

y, y = \frac{6}{y}

13 + \frac{6}{y} y = 6

\frac{x}{\frac{2}{5} ( x - 2 )} = 4 x

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