Solve by Factoring 6/(x+3)=4/(x-3)

$\frac{6}{x + 3} = \frac{4}{x - 3}$

Step 1

Subtract $\frac{4}{x - 3}$ from both sides of the equation.

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

Step 2

Simplify $\frac{6}{x + 3} - \frac{4}{x - 3}$ .

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

$\frac{6}{x + 3} \cdot \frac{x - 3}{x - 3} - \frac{4}{x - 3} = 0$

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

$\frac{6}{x + 3} \cdot \frac{x - 3}{x - 3} - \frac{4}{x - 3} \cdot \frac{x + 3}{x + 3} = 0$

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

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

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

Multiply $\frac{4}{x - 3}$ by $\frac{x + 3}{x + 3}$ .

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

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

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Factor $2$ out of $6 (x - 3) - 4 (x + 3)$ .

Factor $2$ out of $6 (x - 3)$ .

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

Factor $2$ out of $- 4 (x + 3)$ .

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

Factor $2$ out of $2 (3 (x - 3)) + 2 (- 2 (x + 3))$ .

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

Apply the distributive property.

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

Multiply $3$ by $- 3$ .

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

Apply the distributive property.

$\frac{2 (3 x - 9 - 2 x - 2 \cdot 3)}{(x + 3) (x - 3)} = 0$

Multiply $- 2$ by $3$ .

$\frac{2 (3 x - 9 - 2 x - 6)}{(x + 3) (x - 3)} = 0$

Subtract $2 x$ from $3 x$ .

$\frac{2 (x - 9 - 6)}{(x + 3) (x - 3)} = 0$

Subtract $6$ from $- 9$ .

$\frac{2 (x - 15)}{(x + 3) (x - 3)} = 0$

Step 3

Set the numerator equal to zero.

$2 (x - 15) = 0$

Step 4

Solve the equation for $x$ .

Divide each term in $2 (x - 15) = 0$ by $2$ and simplify.

Divide each term in $2 (x - 15) = 0$ by $2$ .

$\frac{2 (x - 15)}{2} = \frac{0}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 (x - 15)}{2} = \frac{0}{2}$

Divide $x - 15$ by $1$ .

$x - 15 = \frac{0}{2}$

Simplify the right side.

Divide $0$ by $2$ .

$x - 15 = 0$

Add $15$ to both sides of the equation.

$x = 15$

Solve by Factoring 6/(x+3)=4/(x-3)

Related Questions

Support LCMGCF.com by disabling your adblocker.