What is the quotient? \( \frac{n+3}{2 n-6}+\frac{n+3}{3 n-9} \) \( \frac{2}{3} \) \( \frac{3}{2} \) \( \frac{(n+3)^{2}}{6(n-3)^{2}} \) \( 0 \frac{6(n-3)^{2}}{(n+3)^{2}} \)

Calculate or simplify the expression \( \frac{n+3}{2n-6}+\frac{n+3}{3n-9} \). Simplify the expression by following steps: - step0: Solution: \(\frac{n+3}{2n-6}+\frac{n+3}{3n-9}\) - step1: Factor the expression: \(\frac{n+3}{2\left(n-3\right)}+\frac{n+3}{3\left(n-3\right)}\) - step2: Reduce fractions to a common denominator: \(\frac{\left(n+3\right)\times 3}{2\left(n-3\right)\times 3}+\frac{\left(n+3\right)\times 2}{3\left(n-3\right)\times 2}\) - step3: Multiply the numbers: \(\frac{\left(n+3\right)\times 3}{6\left(n-3\right)}+\frac{\left(n+3\right)\times 2}{3\left(n-3\right)\times 2}\) - step4: Multiply the numbers: \(\frac{\left(n+3\right)\times 3}{6\left(n-3\right)}+\frac{\left(n+3\right)\times 2}{6\left(n-3\right)}\) - step5: Transform the expression: \(\frac{\left(n+3\right)\times 3+\left(n+3\right)\times 2}{6\left(n-3\right)}\) - step6: Multiply the terms: \(\frac{3n+9+\left(n+3\right)\times 2}{6\left(n-3\right)}\) - step7: Multiply the terms: \(\frac{3n+9+2n+6}{6\left(n-3\right)}\) - step8: Add the terms: \(\frac{5n+15}{6\left(n-3\right)}\) - step9: Simplify: \(\frac{5n+15}{6n-18}\) The quotient of the given expression is \( \frac{5n+15}{6n-18} \).