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

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

Solve for x

$$x=-6$$

Steps for Solving Linear Equation

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

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

Use the distributive property to multiply x-3 by 3x+4 and combine like terms.

$$3x^{2}-5x-12-3\times 2x=x\times 3\left(x-3\right)$$

Multiply -3 and 2 to get -6.

$$3x^{2}-5x-12-6x=x\times 3\left(x-3\right)$$

Combine -5x and -6x to get -11x.

$$3x^{2}-11x-12=x\times 3\left(x-3\right)$$

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

$$3x^{2}-11x-12=3x^{2}-3x\times 3$$

Multiply -3 and 3 to get -9.

$$3x^{2}-11x-12=3x^{2}-9x$$

Subtract 3x^{2} from both sides.

$$3x^{2}-11x-12-3x^{2}=-9x$$

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

$$-11x-12=-9x$$

Add 9x to both sides.

$$-11x-12+9x=0$$

Combine -11x and 9x to get -2x.

$$-2x-12=0$$

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

$$-2x=12$$

Divide both sides by -2.

$$x=\frac{12}{-2}$$

Divide 12 by -2 to get -6.

$$x=-6$$