Questions: Solve for (x). [ frac23-frac5x+3=frac13 x+9 x= ]

Solution Steps

To solve the equation $\frac{2}{3} - \frac{5}{x+3} = \frac{1}{3x+9}$, we can follow these steps:

1. Recognize that $3x + 9$ can be factored as $3(x + 3)$.
2. Rewrite the equation with a common denominator.
3. Solve the resulting equation for $x$.

We start with the equation: $$\frac{2}{3} - \frac{5}{x+3} = \frac{1}{3x+9}$$ Notice that $3x + 9$ can be factored as $3(x + 3)$.

Rewrite the equation with a common denominator: $$\frac{2}{3} - \frac{5}{x+3} = \frac{1}{3(x+3)}$$

Multiply both sides by $3(x + 3)$ to clear the denominators: $$2(x + 3) - 15 = 1$$

Simplify the equation: $$2x + 6 - 15 = 1$$ $$2x - 9 = 1$$ $$2x = 10$$ $$x = 5$$

Final Answer