Question

What is the quotient? n+3/2n-6 divide n+3 /3n-9

Answer 1

(n+3)/(2n-6):(n+3)/(3n-9)=(n+3)/(2(n-3))×(3(n-3))/(n+3)=3/2

Answer 2

ANSWER
The quotient simplifies to
$\frac{3}{2}$



EXPLANATION


We want to find the quotient:

$\frac{n + 3}{2n - 6} \div \frac{n + 3}{3n - 9}$


We need to multiply the first fraction by the reciprocal of the second fraction to obtain,

$\Rightarrow \frac{n + 3}{2n - 6} \div \frac{n + 3}{3n - 9} = \frac{n + 3}{2n - 6} \times \frac{3n - 9}{n + 3}$



We now factor to obtain,

$\Rightarrow\frac{n + 3}{2n - 6} \div \frac{n + 3}{3n - 9} = \frac{n + 3}{2(n - 3)} \times \frac{3(n - 3)}{n + 3}$


We cancel out common factors to obtain,



$\Rightarrow\frac{n + 3}{2n - 6} \div \frac{n + 3}{3n - 9} = \frac{1}{2} \times \frac{3}{1}$


This finally gives us,

$\frac{n + 3}{2n - 6} \div \frac{n + 3}{3n - 9} = \frac{3}{2}$