Find the Quotient ((2m+4)/8)÷((m+2)/6)

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

Split the fraction $\frac{2 m + 4}{8}$ into two fractions.

$\frac{\frac{2 m}{8} + \frac{4}{8}}{\frac{m + 2}{6}}$

Split the fraction $\frac{m + 2}{6}$ into two fractions.

$\frac{\frac{2 m}{8} + \frac{4}{8}}{\frac{m}{6} + \frac{2}{6}}$

Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of $0$ .

$\frac{m}{6}$

$\frac{2}{6}$

$\frac{2 m}{8}$

$\frac{4}{8}$

Divide the highest order term in the dividend $\frac{2 m}{8}$ by the highest order term in divisor $\frac{m}{6}$ .

					$\frac{3}{2}$
	$\frac{m}{6}$	+	$\frac{2}{6}$		$\frac{2 m}{8}$	+	$\frac{4}{8}$

Multiply the new quotient term by the divisor.

The expression needs to be subtracted from the dividend, so change all the signs in $\frac{m}{4} + \frac{1}{2}$

After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.

Since the remander is $0$ , the final answer is the quotient.

$\frac{3}{2}$