Solve by Factoring 2=4/n+1/3

$2 = \frac{4}{n} + \frac{1}{3}$

Step 1

Move all the expressions to the left side of the equation.

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

$2 - \frac{4}{n} = \frac{1}{3}$

Subtract $\frac{1}{3}$ from both sides of the equation.

$2 - \frac{4}{n} - \frac{1}{3} = 0$

Step 2

Simplify $2 - \frac{4}{n} - \frac{1}{3}$ .

To write $2$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- \frac{4}{n} + 2 \cdot \frac{3}{3} - \frac{1}{3} = 0$

Combine $2$ and $\frac{3}{3}$ .

$- \frac{4}{n} + \frac{2 \cdot 3}{3} - \frac{1}{3} = 0$

Combine the numerators over the common denominator.

$- \frac{4}{n} + \frac{2 \cdot 3 - 1}{3} = 0$

Simplify the numerator.

Multiply $2$ by $3$ .

$- \frac{4}{n} + \frac{6 - 1}{3} = 0$

Subtract $1$ from $6$ .

$- \frac{4}{n} + \frac{5}{3} = 0$

Step 3

To write $- \frac{4}{n}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- \frac{4}{n} \cdot \frac{3}{3} + \frac{5}{3} = 0$

Step 4

To write $\frac{5}{3}$ as a fraction with a common denominator, multiply by $\frac{n}{n}$ .

$- \frac{4}{n} \cdot \frac{3}{3} + \frac{5}{3} \cdot \frac{n}{n} = 0$

Step 5

Write each expression with a common denominator of $n \cdot 3$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{4}{n}$ by $\frac{3}{3}$ .

$- \frac{4 \cdot 3}{n \cdot 3} + \frac{5}{3} \cdot \frac{n}{n} = 0$

Multiply $\frac{5}{3}$ by $\frac{n}{n}$ .

$- \frac{4 \cdot 3}{n \cdot 3} + \frac{5 n}{3 n} = 0$

Reorder the factors of $n \cdot 3$ .

$- \frac{4 \cdot 3}{3 n} + \frac{5 n}{3 n} = 0$

Step 6

Combine the numerators over the common denominator.

$\frac{- 4 \cdot 3 + 5 n}{3 n} = 0$

Step 7

Multiply $- 4$ by $3$ .

$\frac{- 12 + 5 n}{3 n} = 0$

Step 8

Set the numerator equal to zero.

$- 12 + 5 n = 0$

Step 9

Solve the equation for $n$ .

Add $12$ to both sides of the equation.

$5 n = 12$

Divide each term in $5 n = 12$ by $5$ and simplify.

Divide each term in $5 n = 12$ by $5$ .

$\frac{5 n}{5} = \frac{12}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 n}{5} = \frac{12}{5}$

Divide $n$ by $1$ .

$n = \frac{12}{5}$

Solve by Factoring 2=4/n+1/3

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