What is the answer to (3x+6)/3-(4x)/(x-3)=x ?

The answer to (3x+6)/3-(4x)/(x-3)=x is x=-3

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(3x+6)/3-(4x)/(x-3)=x

\frac{3 x + 6}{3} - \frac{4 x}{x - 3} = x

x = - 3

Solution steps

\frac{3 x + 6}{3} - \frac{4 x}{x - 3} = x

Simplify

\frac{3 x + 6}{3} : x + 2

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

Multiply both sides by

x - 3

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

Subtract

x (x - 3)

from both sides

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

Simplify

2 (x - 3) - 4 x = 0

Expand

2 (x - 3) - 4 x : - 2 x - 6

- 2 x - 6 = 0

Move

6

to the right side

- 2 x = 6

Divide both sides by

- 2

x = - 3

Verify Solutions

Find undefined (singularity) points:

x = 3

Combine undefined points with solutions:

x = - 3

\frac{5}{2 a} = 3 - \frac{2}{a}

\frac{3}{x} + \frac{7}{x} = x + 3

\frac{1}{6} + \frac{1}{x} = \frac{1}{4}

- \frac{3}{x} = 0

\frac{y + 6}{3 - y} = \frac{5 + 2 y}{7 y - 5}

What is the answer to (3x+6)/3-(4x)/(x-3)=x ?
The answer to (3x+6)/3-(4x)/(x-3)=x is x=-3
Solve for x: (3x+6)/3-(4x)/(x-3)=x
The solution is x=-3