Solve (x-1/x+1)-(x+2/x-2)=0

$$( \frac { x - 1 } { x + 1 } ) - ( \frac { x + 2 } { x - 2 } ) = 0$$

Solve for x

$$x=0$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -1,2 since division by zero is not defined. Multiply both sides of the equation by \left(x-2\right)\left(x+1\right), the least common multiple of x+1,x-2.

$$\left(x-2\right)\left(x-1\right)-\left(x+1\right)\left(x+2\right)=0$$

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

$$x^{2}-3x+2-\left(x+1\right)\left(x+2\right)=0$$

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

$$x^{2}-3x+2-\left(x^{2}+3x+2\right)=0$$

To find the opposite of x^{2}+3x+2, find the opposite of each term.

$$x^{2}-3x+2-x^{2}-3x-2=0$$

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

$$-3x+2-3x-2=0$$

Combine -3x and -3x to get -6x.

$$-6x+2-2=0$$

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.

$$x=0$$