Solve by Factoring 4/(n+2)=7/n

$\frac{4}{n + 2} = \frac{7}{n}$

Step 1

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

$\frac{4}{n + 2} - \frac{7}{n} = 0$

Step 2

Simplify $\frac{4}{n + 2} - \frac{7}{n}$ .

To write $\frac{4}{n + 2}$ as a fraction with a common denominator, multiply by $\frac{n}{n}$ .

$\frac{4}{n + 2} \cdot \frac{n}{n} - \frac{7}{n} = 0$

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

$\frac{4}{n + 2} \cdot \frac{n}{n} - \frac{7}{n} \cdot \frac{n + 2}{n + 2} = 0$

Write each expression with a common denominator of $(n + 2) n$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{4}{n + 2}$ by $\frac{n}{n}$ .

$\frac{4 n}{(n + 2) n} - \frac{7}{n} \cdot \frac{n + 2}{n + 2} = 0$

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

$\frac{4 n}{(n + 2) n} - \frac{7 (n + 2)}{n (n + 2)} = 0$

Reorder the factors of $(n + 2) n$ .

$\frac{4 n}{n (n + 2)} - \frac{7 (n + 2)}{n (n + 2)} = 0$

Combine the numerators over the common denominator.

$\frac{4 n - 7 (n + 2)}{n (n + 2)} = 0$

Simplify the numerator.

Apply the distributive property.

$\frac{4 n - 7 n - 7 \cdot 2}{n (n + 2)} = 0$

Multiply $- 7$ by $2$ .

$\frac{4 n - 7 n - 14}{n (n + 2)} = 0$

Subtract $7 n$ from $4 n$ .

$\frac{- 3 n - 14}{n (n + 2)} = 0$

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

$\frac{- (3 n) - 14}{n (n + 2)} = 0$

Rewrite $- 14$ as $- 1 (14)$ .

$\frac{- (3 n) - 1 (14)}{n (n + 2)} = 0$

Factor $- 1$ out of $- (3 n) - 1 (14)$ .

$\frac{- (3 n + 14)}{n (n + 2)} = 0$

Rewrite $- (3 n + 14)$ as $- 1 (3 n + 14)$ .

$\frac{- 1 (3 n + 14)}{n (n + 2)} = 0$

Move the negative in front of the fraction.

$- \frac{3 n + 14}{n (n + 2)} = 0$

Step 3

Set the numerator equal to zero.

$3 n + 14 = 0$

Step 4

Solve the equation for $n$ .

Subtract $14$ from both sides of the equation.

$3 n = - 14$

Divide each term in $3 n = - 14$ by $3$ and simplify.

Divide each term in $3 n = - 14$ by $3$ .

$\frac{3 n}{3} = \frac{- 14}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 n}{3} = \frac{- 14}{3}$

Divide $n$ by $1$ .

$n = \frac{- 14}{3}$

Simplify the right side.

Move the negative in front of the fraction.

$n = - \frac{14}{3}$

Solve by Factoring 4/(n+2)=7/n

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