Question

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

Explanation:

Step1: Factor the denominators

Factor \(2n - 6\) to \(2(n - 3)\) and \(3n-9\) to \(3(n - 3)\). 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:

\(\frac{3}{2}\)