Answer
$\frac{3x+8}{3x+10}$, $x\ne-3,-\frac{10}{3}$
Work Step by Step
Step 1. To remove the fractions, we can multiply both the numerator and the denominator with a common factor $x+3$.
Step 2. We have $\frac{3-\frac{1}{x+3}}{3+\frac{1}{x+3}}\cdot \frac{x+3}{x+3}=\frac{3x+9-1}{3x+9+1}=\frac{3x+8}{3x+10}$
Step 3. We can identify the domain requirements for the variable as $x\ne-3,-\frac{10}{3}$
Step 4. We conclude the result as $\frac{3x+8}{3x+10}$ with $x\ne-3,-\frac{10}{3}$
