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

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

Step 1

Subtract $x$ from both sides of the equation.

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

Step 2

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

Cancel the common factor of $3 x + 6$ and $3$ .

Factor $3$ out of $3 x$ .

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

Factor $3$ out of $6$ .

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

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

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

Cancel the common factors.

Factor $3$ out of $3$ .

$\frac{3 (x + 2)}{3 (1)} - \frac{4 x}{x - 3} - x = 0$

Cancel the common factor.

$\frac{3 (x + 2)}{3 \cdot 1} - \frac{4 x}{x - 3} - x = 0$

Rewrite the expression.

$\frac{x + 2}{1} - \frac{4 x}{x - 3} - x = 0$

Divide $x + 2$ by $1$ .

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

Combine the opposite terms in $x + 2 - \frac{4 x}{x - 3} - x$ .

Subtract $x$ from $x$ .

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

Add $2 - \frac{4 x}{x - 3}$ and $0$ .

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

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

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

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

Factor $2$ out of $- 4 x$ .

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

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

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

Subtract $2 x$ from $x$ .

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

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

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

Rewrite $- 3$ as $- 1 (3)$ .

$\frac{2 (- (x) - 1 (3))}{x - 3} = 0$

Factor $- 1$ out of $- (x) - 1 (3)$ .

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

Rewrite $- (x + 3)$ as $- 1 (x + 3)$ .

$\frac{2 (- 1 (x + 3))}{x - 3} = 0$

Move the negative in front of the fraction.

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

Step 3

Set the numerator equal to zero.

$2 (x + 3) = 0$

Step 4

Solve the equation for $x$ .

Divide each term in $2 (x + 3) = 0$ by $2$ and simplify.

Divide each term in $2 (x + 3) = 0$ by $2$ .

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $x + 3$ by $1$ .

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

Simplify the right side.

Divide $0$ by $2$ .

$x + 3 = 0$

Subtract $3$ from both sides of the equation.

$x = - 3$

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

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