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

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

Solve for x

$$x=-3$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -2,6 since division by zero is not defined. Multiply both sides of the equation by \left(x-6\right)\left(x+2\right), the least common multiple of x-6,x+2.

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

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

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

Use the distributive property to multiply 3x+6 by x.

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

Use the distributive property to multiply x-6 by 2.

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

To find the opposite of 2x-12, find the opposite of each term.

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

Combine 6x and -2x to get 4x.

$$3x^{2}+4x+12=3\left(x-6\right)\left(x+2\right)$$

Use the distributive property to multiply 3 by x-6.

$$3x^{2}+4x+12=\left(3x-18\right)\left(x+2\right)$$

Use the distributive property to multiply 3x-18 by x+2 and combine like terms.

$$3x^{2}+4x+12=3x^{2}-12x-36$$

Subtract 3x^{2} from both sides.

$$3x^{2}+4x+12-3x^{2}=-12x-36$$

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

$$4x+12=-12x-36$$

Add 12x to both sides.

$$4x+12+12x=-36$$

Combine 4x and 12x to get 16x.

$$16x+12=-36$$

Subtract 12 from both sides.

$$16x=-36-12$$

Subtract 12 from -36 to get -48.

$$16x=-48$$

Divide both sides by 16.

$$x=\frac{-48}{16}$$

Divide -48 by 16 to get -3.

$$x=-3$$