Question

what is the quotient?
\\(\frac{2m + 4}{8} div \frac{m + 2}{6}\\)
\\(\bigcirc \frac{24}{(m + 2)^2}\\)
\\(\bigcirc \frac{(m + 2)^2}{24}\\)
\\(\bigcirc \frac{2}{3}\\)
\\(\bigcirc \frac{3}{2}\\)

Explanation:

Step1: Rewrite division as multiplication

$\frac{2m+4}{8} \div \frac{m+2}{6} = \frac{2m+4}{8} \times \frac{6}{m+2}$

Step2: Factor numerator of first term

$\frac{2(m+2)}{8} \times \frac{6}{m+2}$

Step3: Cancel common factor $(m+2)$

$\frac{2}{8} \times 6$

Step4: Simplify fractions and multiply

$\frac{2 \times 6}{8} = \frac{12}{8} = \frac{3}{2}$

Answer:

D. $\frac{3}{2}$