Solve for: /(2) 8 = /(n+4) n-4

Expression: $$\frac { 2 } { 8 } = \frac { n + 4 } { n - 4 }$$

Variable $n$ cannot be equal to $4$ since division by zero is not defined. Multiply both sides of the equation by $8\left(n-4\right)$, the least common multiple of $8,n-4$.

$$\left(n-4\right)\times 2=8\left(n+4\right)$$

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

$$2n-8=8\left(n+4\right)$$

Use the distributive property to multiply $8$ by $n+4$.

$$2n-8=8n+32$$

Subtract $8n$ from both sides.

$$2n-8-8n=32$$

Combine $2n$ and $-8n$ to get $-6n$.

$$-6n-8=32$$

Add $8$ to both sides.

$$-6n=32+8$$

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

$$-6n=40$$

Divide both sides by $-6$.

$$n=\frac{40}{-6}$$

Reduce the fraction $\frac{40}{-6}$ to lowest terms by extracting and canceling out $2$.

$$n=-\frac{20}{3}$$