what is the quotient?\n$\frac{n + 3}{2n - 6}div\frac{n + 3}{3n - 9}$\n$\frac{2}{3}$\n$\frac{3}{2}$\n$\frac{(n…

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

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

Answer

Explanation:

Step1: Factor the denominators

Factor (2n - 6=2(n - 3)) and (3n - 9 = 3(n - 3)). The expression becomes (\frac{n + 3}{2(n - 3)}\div\frac{n + 3}{3(n - 3)}).

Step2: Change division to multiplication

Recall that dividing by a fraction is the same as multiplying by its reciprocal. So (\frac{n + 3}{2(n - 3)}\div\frac{n + 3}{3(n - 3)}=\frac{n + 3}{2(n - 3)}\times\frac{3(n - 3)}{n + 3}).

Step3: Cancel out common factors

Cancel out the common factors ((n + 3)) and ((n - 3)) in the numerator and denominator. We get (\frac{3}{2}).

Answer:

(\frac{3}{2})