Solve by Factoring 6/x=7/(x+3)

$\frac{6}{x} = \frac{7}{x + 3}$

Step 1

Subtract $\frac{7}{x + 3}$ from both sides of the equation.

$\frac{6}{x} - \frac{7}{x + 3} = 0$

Step 2

Simplify $\frac{6}{x} - \frac{7}{x + 3}$ .

To write $\frac{6}{x}$ as a fraction with a common denominator, multiply by $\frac{x + 3}{x + 3}$ .

$\frac{6}{x} \cdot \frac{x + 3}{x + 3} - \frac{7}{x + 3} = 0$

To write $- \frac{7}{x + 3}$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

$\frac{6}{x} \cdot \frac{x + 3}{x + 3} - \frac{7}{x + 3} \cdot \frac{x}{x} = 0$

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

Multiply $\frac{6}{x}$ by $\frac{x + 3}{x + 3}$ .

$\frac{6 (x + 3)}{x (x + 3)} - \frac{7}{x + 3} \cdot \frac{x}{x} = 0$

Multiply $\frac{7}{x + 3}$ by $\frac{x}{x}$ .

$\frac{6 (x + 3)}{x (x + 3)} - \frac{7 x}{(x + 3) x} = 0$

Reorder the factors of $(x + 3) x$ .

$\frac{6 (x + 3)}{x (x + 3)} - \frac{7 x}{x (x + 3)} = 0$

Combine the numerators over the common denominator.

$\frac{6 (x + 3) - 7 x}{x (x + 3)} = 0$

Simplify the numerator.

Apply the distributive property.

$\frac{6 x + 6 \cdot 3 - 7 x}{x (x + 3)} = 0$

Multiply $6$ by $3$ .

$\frac{6 x + 18 - 7 x}{x (x + 3)} = 0$

Subtract $7 x$ from $6 x$ .

$\frac{- x + 18}{x (x + 3)} = 0$

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

$\frac{- (x) + 18}{x (x + 3)} = 0$

Rewrite $18$ as $- 1 (- 18)$ .

$\frac{- (x) - 1 (- 18)}{x (x + 3)} = 0$

Factor $- 1$ out of $- (x) - 1 (- 18)$ .

$\frac{- (x - 18)}{x (x + 3)} = 0$

Rewrite $- (x - 18)$ as $- 1 (x - 18)$ .

$\frac{- 1 (x - 18)}{x (x + 3)} = 0$

Move the negative in front of the fraction.

$- \frac{x - 18}{x (x + 3)} = 0$

Step 3

Set the numerator equal to zero.

$x - 18 = 0$

Step 4

Add $18$ to both sides of the equation.

$x = 18$