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

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

Solve for x

$$x=-3$$

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}-4,x-2.

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

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

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

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.

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

Subtract x^{2} from both sides.

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

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

$$2+2x=-4$$

Subtract 2 from both sides.

$$2x=-4-2$$

Subtract 2 from -4 to get -6.

$$2x=-6$$

Divide both sides by 2.

$$x=\frac{-6}{2}$$

Divide -6 by 2 to get -3.

$$x=-3$$