Solve by Factoring x/(x+3)=3/19

$\frac{x}{x + 3} = \frac{3}{19}$

Step 1

Subtract $\frac{3}{19}$ from both sides of the equation.

$\frac{x}{x + 3} - \frac{3}{19} = 0$

Step 2

Simplify $\frac{x}{x + 3} - \frac{3}{19}$ .

To write $\frac{x}{x + 3}$ as a fraction with a common denominator, multiply by $\frac{19}{19}$ .

$\frac{x}{x + 3} \cdot \frac{19}{19} - \frac{3}{19} = 0$

To write $- \frac{3}{19}$ as a fraction with a common denominator, multiply by $\frac{x + 3}{x + 3}$ .

$\frac{x}{x + 3} \cdot \frac{19}{19} - \frac{3}{19} \cdot \frac{x + 3}{x + 3} = 0$

Write each expression with a common denominator of $(x + 3) \cdot 19$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{x}{x + 3}$ by $\frac{19}{19}$ .

$\frac{x \cdot 19}{(x + 3) \cdot 19} - \frac{3}{19} \cdot \frac{x + 3}{x + 3} = 0$

Multiply $\frac{3}{19}$ by $\frac{x + 3}{x + 3}$ .

$\frac{x \cdot 19}{(x + 3) \cdot 19} - \frac{3 (x + 3)}{19 (x + 3)} = 0$

Reorder the factors of $(x + 3) \cdot 19$ .

$\frac{x \cdot 19}{19 (x + 3)} - \frac{3 (x + 3)}{19 (x + 3)} = 0$

Combine the numerators over the common denominator.

$\frac{x \cdot 19 - 3 (x + 3)}{19 (x + 3)} = 0$

Simplify the numerator.

Move $19$ to the left of $x$ .

$\frac{19 \cdot x - 3 (x + 3)}{19 (x + 3)} = 0$

Apply the distributive property.

$\frac{19 x - 3 x - 3 \cdot 3}{19 (x + 3)} = 0$

Multiply $- 3$ by $3$ .

$\frac{19 x - 3 x - 9}{19 (x + 3)} = 0$

Subtract $3 x$ from $19 x$ .

$\frac{16 x - 9}{19 (x + 3)} = 0$

Step 3

Set the numerator equal to zero.

$16 x - 9 = 0$

Step 4

Solve the equation for $x$ .

Add $9$ to both sides of the equation.

$16 x = 9$

Divide each term in $16 x = 9$ by $16$ and simplify.

Divide each term in $16 x = 9$ by $16$ .

$\frac{16 x}{16} = \frac{9}{16}$

Simplify the left side.

Cancel the common factor of $16$ .

Cancel the common factor.

$\frac{16 x}{16} = \frac{9}{16}$

Divide $x$ by $1$ .

$x = \frac{9}{16}$