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

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

Solve for x

$$x=0$$

Steps by Finding Square Root

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.

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

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

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

Subtract x from both sides.

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

Combine x and -x to get 0.

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

Add 2 to both sides.

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

Add -2 and 2 to get 0.

$$x^{2}=0$$

Take the square root of both sides of the equation.

$$x=0 x=0$$

The equation is now solved. Solutions are the same.

$$x=0$$

Steps Using the Quadratic Formula

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.

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

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

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

Subtract x from both sides.

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

Combine x and -x to get 0.

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

Add 2 to both sides.

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

Add -2 and 2 to get 0.

$$x^{2}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}}}{2}$$

Take the square root of 0^{2}.

$$x=\frac{0±0}{2}$$

Divide 0 by 2.

$$x=0$$