Solve by Factoring 5/x=10/(3x)+4

$\frac{5}{x} = \frac{10}{3 x} + 4$

Step 1

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

Subtract $\frac{10}{3 x}$ from both sides of the equation.

$\frac{5}{x} - \frac{10}{3 x} = 4$

Subtract $4$ from both sides of the equation.

$\frac{5}{x} - \frac{10}{3 x} - 4 = 0$

Step 2

Simplify $\frac{5}{x} - \frac{10}{3 x} - 4$ .

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

$\frac{5}{x} \cdot \frac{3}{3} - \frac{10}{3 x} - 4 = 0$

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

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

$\frac{5 \cdot 3}{x \cdot 3} - \frac{10}{3 x} - 4 = 0$

Move $3$ to the left of $x$ .

$\frac{5 \cdot 3}{3 x} - \frac{10}{3 x} - 4 = 0$

Combine the numerators over the common denominator.

$\frac{5 \cdot 3 - 10}{3 x} - 4 = 0$

Simplify the numerator.

Multiply $5$ by $3$ .

$\frac{15 - 10}{3 x} - 4 = 0$

Subtract $10$ from $15$ .

$\frac{5}{3 x} - 4 = 0$

Step 3

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

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

Step 4

Combine $- 4$ and $\frac{3 x}{3 x}$ .

$\frac{5}{3 x} + \frac{- 4 (3 x)}{3 x} = 0$

Step 5

Combine the numerators over the common denominator.

$\frac{5 - 4 (3 x)}{3 x} = 0$

Step 6

Remove parentheses.

$\frac{5 - 4 \cdot (3 x)}{3 x} = 0$

Step 7

Multiply $- 4$ by $3$ .

$\frac{5 - 12 x}{3 x} = 0$

Step 8

Set the numerator equal to zero.

$5 - 12 x = 0$

Step 9

Solve the equation for $x$ .

Subtract $5$ from both sides of the equation.

$- 12 x = - 5$

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

Divide each term in $- 12 x = - 5$ by $- 12$ .

$\frac{- 12 x}{- 12} = \frac{- 5}{- 12}$

Simplify the left side.

Cancel the common factor of $- 12$ .

Cancel the common factor.

$\frac{- 12 x}{- 12} = \frac{- 5}{- 12}$

Divide $x$ by $1$ .

$x = \frac{- 5}{- 12}$

Simplify the right side.

Dividing two negative values results in a positive value.

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

Solve by Factoring 5/x=10/(3x)+4

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