Solve x+1/x-2=x-1/x+2

$$\frac{ x+1 }{ x-2 } = \frac{ x-1 }{ x+2 }$$

Solve for x

$$x=0$$

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.

$$\left(x+2\right)\left(x+1\right)=\left(x-2\right)\left(x-1\right)$$

Use the distributive property to multiply x+2 by x+1 and combine like terms.

$$x^{2}+3x+2=\left(x-2\right)\left(x-1\right)$$

Use the distributive property to multiply x-2 by x-1 and combine like terms.

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

Subtract x^{2} from both sides.

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

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

$$3x+2=-3x+2$$

Add 3x to both sides.

$$3x+2+3x=2$$

Combine 3x and 3x to get 6x.

$$6x+2=2$$

Subtract 2 from both sides.

$$6x=2-2$$

Subtract 2 from 2 to get 0.

$$6x=0$$

Product of two numbers is equal to 0 if at least one of them is 0. Since 6 is not equal to 0, x must be equal to 0.

$$x=0$$