Solve x/3+x+2/x-4=x^2/3x-12

$$\frac { x } { 3 } + \frac { x + 2 } { x - 4 } = \frac { x ^ { 2 } } { 3 x - 12 }$$

Solve for x

$$x=6$$

Steps for Solving Linear Equation

Variable x cannot be equal to 4 since division by zero is not defined. Multiply both sides of the equation by 3\left(x-4\right), the least common multiple of 3,x-4,3x-12.

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

Use the distributive property to multiply x-4 by x.

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

Use the distributive property to multiply 3 by x+2.

$$x^{2}-4x+3x+6=x^{2}$$

Combine -4x and 3x to get -x.

$$x^{2}-x+6=x^{2}$$

Subtract x^{2} from both sides.

$$x^{2}-x+6-x^{2}=0$$

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

$$-x+6=0$$

Subtract 6 from both sides. Anything subtracted from zero gives its negation.

$$-x=-6$$

Multiply both sides by -1.

$$x=6$$