We need to solve the equation $\frac{3}{x+7} - \frac{1}{x+2} = 0$.

1. Problem Description

We need to solve the equation $\frac{3}{x+7} - \frac{1}{x+2} = 0$.

2. Solution Steps

To solve the equation $\frac{3}{x+7} - \frac{1}{x+2} = 0$, we first add $\frac{1}{x+2}$ to both sides of the equation to get

$\frac{3}{x+7} = \frac{1}{x+2}$

Next, cross-multiply to get

$3(x+2) = 1(x+7)$

Expanding both sides gives

$3x + 6 = x + 7$

Subtracting $x$ from both sides gives

$2x + 6 = 7$

Subtracting $6$ from both sides gives

$2x = 1$

Dividing by $2$ gives

$x = \frac{1}{2}$

We need to check if this solution is valid by making sure it doesn't make any denominator zero.

$x+7 = \frac{1}{2} + 7 = \frac{15}{2} \neq 0$

$x+2 = \frac{1}{2} + 2 = \frac{5}{2} \neq 0$

So the solution is valid.

3. Final Answer

$x = \frac{1}{2}$