Solve by Factoring 2/8=(n+4)/(n-4)

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

Step 1

Subtract $\frac{n + 4}{n - 4}$ from both sides of the equation.

$\frac{2}{8} - \frac{n + 4}{n - 4} = 0$

Step 2

Simplify $\frac{2}{8} - \frac{n + 4}{n - 4}$ .

Cancel the common factor of $2$ and $8$ .

Factor $2$ out of $2$ .

$\frac{2 (1)}{8} - \frac{n + 4}{n - 4} = 0$

Cancel the common factors.

Factor $2$ out of $8$ .

$\frac{2 \cdot 1}{2 \cdot 4} - \frac{n + 4}{n - 4} = 0$

Cancel the common factor.

$\frac{2 \cdot 1}{2 \cdot 4} - \frac{n + 4}{n - 4} = 0$

Rewrite the expression.

$\frac{1}{4} - \frac{n + 4}{n - 4} = 0$

To write $\frac{1}{4}$ as a fraction with a common denominator, multiply by $\frac{n - 4}{n - 4}$ .

$\frac{1}{4} \cdot \frac{n - 4}{n - 4} - \frac{n + 4}{n - 4} = 0$

To write $- \frac{n + 4}{n - 4}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{1}{4} \cdot \frac{n - 4}{n - 4} - \frac{n + 4}{n - 4} \cdot \frac{4}{4} = 0$

Write each expression with a common denominator of $4 (n - 4)$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{4}$ by $\frac{n - 4}{n - 4}$ .

$\frac{n - 4}{4 (n - 4)} - \frac{n + 4}{n - 4} \cdot \frac{4}{4} = 0$

Multiply $\frac{n + 4}{n - 4}$ by $\frac{4}{4}$ .

$\frac{n - 4}{4 (n - 4)} - \frac{(n + 4) \cdot 4}{(n - 4) \cdot 4} = 0$

Reorder the factors of $(n - 4) \cdot 4$ .

$\frac{n - 4}{4 (n - 4)} - \frac{(n + 4) \cdot 4}{4 (n - 4)} = 0$

Combine the numerators over the common denominator.

$\frac{n - 4 - (n + 4) \cdot 4}{4 (n - 4)} = 0$

Simplify the numerator.

Apply the distributive property.

$\frac{n - 4 + (- n - 1 \cdot 4) \cdot 4}{4 (n - 4)} = 0$

Multiply $- 1$ by $4$ .

$\frac{n - 4 + (- n - 4) \cdot 4}{4 (n - 4)} = 0$

Apply the distributive property.

$\frac{n - 4 - n \cdot 4 - 4 \cdot 4}{4 (n - 4)} = 0$

Multiply $4$ by $- 1$ .

$\frac{n - 4 - 4 n - 4 \cdot 4}{4 (n - 4)} = 0$

Multiply $- 4$ by $4$ .

$\frac{n - 4 - 4 n - 16}{4 (n - 4)} = 0$

Subtract $4 n$ from $n$ .

$\frac{- 3 n - 4 - 16}{4 (n - 4)} = 0$

Subtract $16$ from $- 4$ .

$\frac{- 3 n - 20}{4 (n - 4)} = 0$

Factor $- 1$ out of $- 3 n$ .

$\frac{- (3 n) - 20}{4 (n - 4)} = 0$

Rewrite $- 20$ as $- 1 (20)$ .

$\frac{- (3 n) - 1 (20)}{4 (n - 4)} = 0$

Factor $- 1$ out of $- (3 n) - 1 (20)$ .

$\frac{- (3 n + 20)}{4 (n - 4)} = 0$

Rewrite $- (3 n + 20)$ as $- 1 (3 n + 20)$ .

$\frac{- 1 (3 n + 20)}{4 (n - 4)} = 0$

Move the negative in front of the fraction.

$- \frac{3 n + 20}{4 (n - 4)} = 0$

Step 3

Set the numerator equal to zero.

$3 n + 20 = 0$

Step 4

Solve the equation for $n$ .

Subtract $20$ from both sides of the equation.

$3 n = - 20$

Divide each term in $3 n = - 20$ by $3$ and simplify.

Divide each term in $3 n = - 20$ by $3$ .

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

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

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

Divide $n$ by $1$ .

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

Simplify the right side.

Move the negative in front of the fraction.

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

Solve by Factoring 2/8=(n+4)/(n-4)

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