Solve 3x+6/3-4x/x-2=x

$$\frac { 3 x + 6 } { 3 } - \frac { 4 x } { x - 2 } = x$$

Solve for x

$$x=-2$$

Steps for Solving Linear Equation

Variable x cannot be equal to 2 since division by zero is not defined. Multiply both sides of the equation by 3\left(x-2\right), the least common multiple of 3,x-2.

$$\left(x-2\right)\left(3x+6\right)-3\times 4x=x\times 3\left(x-2\right)$$

Use the distributive property to multiply x-2 by 3x+6 and combine like terms.

$$3x^{2}-12-3\times 4x=x\times 3\left(x-2\right)$$

Multiply -3 and 4 to get -12.

$$3x^{2}-12-12x=x\times 3\left(x-2\right)$$

Use the distributive property to multiply x\times 3 by x-2.

$$3x^{2}-12-12x=3x^{2}-2x\times 3$$

Multiply -2 and 3 to get -6.

$$3x^{2}-12-12x=3x^{2}-6x$$

Subtract 3x^{2} from both sides.

$$3x^{2}-12-12x-3x^{2}=-6x$$

Combine 3x^{2} and -3x^{2} to get 0.

$$-12-12x=-6x$$

Add 6x to both sides.

$$-12-12x+6x=0$$

Combine -12x and 6x to get -6x.

$$-12-6x=0$$

Add 12 to both sides. Anything plus zero gives itself.

$$-6x=12$$

Divide both sides by -6.

$$x=\frac{12}{-6}$$

Divide 12 by -6 to get -2.

$$x=-2$$