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

Question

UpStudy AI · Accepted Answer

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:
  $$\frac{n+3}{2\left(n-3ight)}+\frac{n+3}{3\left(n-3ight)}$$
- step2: Reduce fractions to a common denominator:
  $$\frac{\left(n+3ight)	imes 3}{2\left(n-3ight)	imes 3}+\frac{\left(n+3ight)	imes 2}{3\left(n-3ight)	imes 2}$$
- step3: Multiply the numbers:
  $$\frac{\left(n+3ight)	imes 3}{6\left(n-3ight)}+\frac{\left(n+3ight)	imes 2}{3\left(n-3ight)	imes 2}$$
- step4: Multiply the numbers:
  $$\frac{\left(n+3ight)	imes 3}{6\left(n-3ight)}+\frac{\left(n+3ight)	imes 2}{6\left(n-3ight)}$$
- step5: Transform the expression:
  $$\frac{\left(n+3ight)	imes 3+\left(n+3ight)	imes 2}{6\left(n-3ight)}$$
- step6: Multiply the terms:
  $$\frac{3n+9+\left(n+3ight)	imes 2}{6\left(n-3ight)}$$
- step7: Multiply the terms:
  $$\frac{3n+9+2n+6}{6\left(n-3ight)}$$
- step8: Add the terms:
  $$\frac{5n+15}{6\left(n-3ight)}$$
- step9: Simplify:
  $$\frac{5n+15}{6n-18}$$
The quotient of the given expression is $$ \frac{5n+15}{6n-18} $$.
The quotient is $$ \frac{5n+15}{6n-18} $$.

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

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