Solve by Factoring (n-5)/(n+8)=2/7

$\frac{n - 5}{n + 8} = \frac{2}{7}$

Step 1

Subtract $\frac{2}{7}$ from both sides of the equation.

$\frac{n - 5}{n + 8} - \frac{2}{7} = 0$

Step 2

Simplify $\frac{n - 5}{n + 8} - \frac{2}{7}$ .

To write $\frac{n - 5}{n + 8}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{n - 5}{n + 8} \cdot \frac{7}{7} - \frac{2}{7} = 0$

To write $- \frac{2}{7}$ as a fraction with a common denominator, multiply by $\frac{n + 8}{n + 8}$ .

$\frac{n - 5}{n + 8} \cdot \frac{7}{7} - \frac{2}{7} \cdot \frac{n + 8}{n + 8} = 0$

Write each expression with a common denominator of $(n + 8) \cdot 7$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{n - 5}{n + 8}$ by $\frac{7}{7}$ .

$\frac{(n - 5) \cdot 7}{(n + 8) \cdot 7} - \frac{2}{7} \cdot \frac{n + 8}{n + 8} = 0$

Multiply $\frac{2}{7}$ by $\frac{n + 8}{n + 8}$ .

$\frac{(n - 5) \cdot 7}{(n + 8) \cdot 7} - \frac{2 (n + 8)}{7 (n + 8)} = 0$

Reorder the factors of $(n + 8) \cdot 7$ .

$\frac{(n - 5) \cdot 7}{7 (n + 8)} - \frac{2 (n + 8)}{7 (n + 8)} = 0$

Combine the numerators over the common denominator.

$\frac{(n - 5) \cdot 7 - 2 (n + 8)}{7 (n + 8)} = 0$

Simplify the numerator.

Apply the distributive property.

$\frac{n \cdot 7 - 5 \cdot 7 - 2 (n + 8)}{7 (n + 8)} = 0$

Move $7$ to the left of $n$ .

$\frac{7 \cdot n - 5 \cdot 7 - 2 (n + 8)}{7 (n + 8)} = 0$

Multiply $- 5$ by $7$ .

$\frac{7 \cdot n - 35 - 2 (n + 8)}{7 (n + 8)} = 0$

Apply the distributive property.

$\frac{7 n - 35 - 2 n - 2 \cdot 8}{7 (n + 8)} = 0$

Multiply $- 2$ by $8$ .

$\frac{7 n - 35 - 2 n - 16}{7 (n + 8)} = 0$

Subtract $2 n$ from $7 n$ .

$\frac{5 n - 35 - 16}{7 (n + 8)} = 0$

Subtract $16$ from $- 35$ .

$\frac{5 n - 51}{7 (n + 8)} = 0$

Step 3

Set the numerator equal to zero.

$5 n - 51 = 0$

Step 4

Solve the equation for $n$ .

Add $51$ to both sides of the equation.

$5 n = 51$

Divide each term in $5 n = 51$ by $5$ and simplify.

Divide each term in $5 n = 51$ by $5$ .

$\frac{5 n}{5} = \frac{51}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 n}{5} = \frac{51}{5}$

Divide $n$ by $1$ .

$n = \frac{51}{5}$

Solve by Factoring (n-5)/(n+8)=2/7

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