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

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

Solve for x

$$x=\frac{2}{3}\approx 0.666666667$$

Steps for Solving Linear Equation

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

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

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

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

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

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

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

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

Use the distributive property to multiply x^{2}-4 by -2.

$$x-x^{2}+6=x^{2}-2x-2x^{2}+8$$

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

$$x-x^{2}+6=-x^{2}-2x+8$$

Add x^{2} to both sides.

$$x-x^{2}+6+x^{2}=-2x+8$$

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

$$x+6=-2x+8$$

Add 2x to both sides.

$$x+6+2x=8$$

Combine x and 2x to get 3x.

$$3x+6=8$$

Subtract 6 from both sides.

$$3x=8-6$$

Subtract 6 from 8 to get 2.

$$3x=2$$

Divide both sides by 3.

$$x=\frac{2}{3}$$