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

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

Solve for x

$$x=8$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values 2,4 since division by zero is not defined. Multiply both sides of the equation by \left(x-4\right)\left(x-2\right), the least common multiple of x-4,x-2.

$$\left(x-2\right)x=\left(x-4\right)\left(x+4\right)$$

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

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

Consider \left(x-4\right)\left(x+4\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 4.

$$x^{2}-2x=x^{2}-16$$

Subtract x^{2} from both sides.

$$x^{2}-2x-x^{2}=-16$$

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

$$-2x=-16$$

Divide both sides by -2.

$$x=\frac{-16}{-2}$$

Divide -16 by -2 to get 8.

$$x=8$$