What is the answer to (2x+5)/2-(3x)/(x-2)=x ?

The answer to (2x+5)/2-(3x)/(x-2)=x is x=-10

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(2x+5)/2-(3x)/(x-2)=x

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

x = - 10

Solution steps

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

Multiply by LCM

2 x^{2} - 5 x - 10 = 2 x^{2} - 4 x

Move

10

to the right side

2 x^{2} - 5 x = 2 x^{2} - 4 x + 10

Subtract

2 x^{2} - 4 x

from both sides

2 x^{2} - 5 x - (2 x^{2} - 4 x) = 2 x^{2} - 4 x + 10 - (2 x^{2} - 4 x)

Simplify

- x = 10

Divide both sides by

- 1

x = - 10

Verify Solutions

Find undefined (singularity) points:

x = 2

Combine undefined points with solutions:

x = - 10

\frac{3}{x} + \frac{4}{2 x} = x - 1

x - 1 = \frac{x ^{2} - 4 x + 3}{x + 2}

\frac{x ^{2} - 10}{x - 1} = \frac{- 14 - 5 x}{x - 1}

\frac{1}{x ^{2} - 2 x - 7} = 1

1 + \frac{x ^{2} - 5 x - 24}{3 x} = \frac{x - 6}{3 x}

What is the answer to (2x+5)/2-(3x)/(x-2)=x ?
The answer to (2x+5)/2-(3x)/(x-2)=x is x=-10
Solve for x: (2x+5)/2-(3x)/(x-2)=x
The solution is x=-10