Evaluate: /(20) x-/(20) x-2 = /(4) x

Expression: $$\frac { 20 } { x } - \frac { 20 } { x - 2 } = \frac { 4 } { x }$$

Variable $x$ cannot be equal to any of the values $0,2$ since division by zero is not defined. Multiply both sides of the equation by $x\left(x-2\right)$, the least common multiple of $x,x-2$.

$$\left(x-2\right)\times 20-x\times 20=\left(x-2\right)\times 4$$

Use the distributive property to multiply $x-2$ by $20$.

$$20x-40-x\times 20=\left(x-2\right)\times 4$$

Use the distributive property to multiply $x-2$ by $4$.

$$20x-40-x\times 20=4x-8$$

Subtract $4x$ from both sides.

$$20x-40-x\times 20-4x=-8$$

Combine $20x$ and $-4x$ to get $16x$.

$$16x-40-x\times 20=-8$$

Add $40$ to both sides.

$$16x-x\times 20=-8+40$$

Add $-8$ and $40$ to get $32$.

$$16x-x\times 20=32$$

Multiply $-1$ and $20$ to get $-20$.

$$16x-20x=32$$

Combine $16x$ and $-20x$ to get $-4x$.

$$-4x=32$$

Divide both sides by $-4$.

$$x=\frac{32}{-4}$$

Divide $32$ by $-4$ to get $-8$.

$$x=-8$$