What is the answer to (2x+4)/2-(3x)/(x-4)=x ?

The answer to (2x+4)/2-(3x)/(x-4)=x is x=-8

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(2x+4)/2-(3x)/(x-4)=x

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

x = - 8

Solution steps

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

Simplify

\frac{2 x + 4}{2} : x + 2

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

Multiply both sides by

x - 4

x (x - 4) + 2 (x - 4) - 3 x = x (x - 4)

Subtract

x (x - 4)

from both sides

x (x - 4) + 2 (x - 4) - 3 x - x (x - 4) = x (x - 4) - x (x - 4)

Simplify

2 (x - 4) - 3 x = 0

Expand

2 (x - 4) - 3 x : - x - 8

- x - 8 = 0

Move

8

to the right side

- x = 8

Divide both sides by

- 1

x = - 8

Verify Solutions

Find undefined (singularity) points:

x = 4

Combine undefined points with solutions:

x = - 8

\frac{3}{2} = \frac{13}{x} - \frac{2}{3}

\frac{5}{4 x + 3} = \frac{5}{4 x} + \frac{5}{3}

x, \frac{3 x + 1}{x} = 2 x + 1

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

\frac{4}{x + 8} = \frac{6}{x}

What is the answer to (2x+4)/2-(3x)/(x-4)=x ?
The answer to (2x+4)/2-(3x)/(x-4)=x is x=-8
Solve for x: (2x+4)/2-(3x)/(x-4)=x
The solution is x=-8