Solve 1=x^2/x^2-4-x/x-2+2/x+2=

$$1 = \frac { x ^ { 2 } } { x ^ { 2 } - 4 } - \frac { x } { x - 2 } + \frac { 2 } { x + 2 } =$$

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}-4,x-2,x+2.

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

Consider \left(x-2\right)\left(x+2\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 2.

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

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

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

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

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

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

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

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

$$x^{2}-4=-2x+2x-4$$

Combine -2x and 2x to get 0.

$$x^{2}-4=-4$$

Add 4 to both sides.

$$x^{2}=-4+4$$

Add -4 and 4 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}-4,x-2,x+2.

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

Consider \left(x-2\right)\left(x+2\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 2.

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

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

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

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

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

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

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

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

$$x^{2}-4=-2x+2x-4$$

Combine -2x and 2x to get 0.

$$x^{2}-4=-4$$

Add 4 to both sides.

$$x^{2}-4+4=0$$

Add -4 and 4 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.

$$x=0$$