Solve by Factoring 9/(3x)=4/(x+2)

$\frac{9}{3 x} = \frac{4}{x + 2}$

Step 1

Subtract $\frac{4}{x + 2}$ from both sides of the equation.

$\frac{9}{3 x} - \frac{4}{x + 2} = 0$

Step 2

Simplify $\frac{9}{3 x} - \frac{4}{x + 2}$ .

Cancel the common factor of $9$ and $3$ .

Factor $3$ out of $9$ .

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

Cancel the common factors.

Factor $3$ out of $3 x$ .

$\frac{3 \cdot 3}{3 (x)} - \frac{4}{x + 2} = 0$

Cancel the common factor.

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

Rewrite the expression.

$\frac{3}{x} - \frac{4}{x + 2} = 0$

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

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

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

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

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

Multiply $\frac{3}{x}$ by $\frac{x + 2}{x + 2}$ .

$\frac{3 (x + 2)}{x (x + 2)} - \frac{4}{x + 2} \cdot \frac{x}{x} = 0$

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

$\frac{3 (x + 2)}{x (x + 2)} - \frac{4 x}{(x + 2) x} = 0$

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

$\frac{3 (x + 2)}{x (x + 2)} - \frac{4 x}{x (x + 2)} = 0$

Combine the numerators over the common denominator.

$\frac{3 (x + 2) - 4 x}{x (x + 2)} = 0$

Simplify the numerator.

Apply the distributive property.

$\frac{3 x + 3 \cdot 2 - 4 x}{x (x + 2)} = 0$

Multiply $3$ by $2$ .

$\frac{3 x + 6 - 4 x}{x (x + 2)} = 0$

Subtract $4 x$ from $3 x$ .

$\frac{- x + 6}{x (x + 2)} = 0$

Factor $- 1$ out of $- x$ .

$\frac{- (x) + 6}{x (x + 2)} = 0$

Rewrite $6$ as $- 1 (- 6)$ .

$\frac{- (x) - 1 (- 6)}{x (x + 2)} = 0$

Factor $- 1$ out of $- (x) - 1 (- 6)$ .

$\frac{- (x - 6)}{x (x + 2)} = 0$

Rewrite $- (x - 6)$ as $- 1 (x - 6)$ .

$\frac{- 1 (x - 6)}{x (x + 2)} = 0$

Move the negative in front of the fraction.

$- \frac{x - 6}{x (x + 2)} = 0$

Step 3

Set the numerator equal to zero.

$x - 6 = 0$

Step 4

Add $6$ to both sides of the equation.

$x = 6$

Solve by Factoring 9/(3x)=4/(x+2)

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