Divide ((2r)/(r+6))÷((2r)/(7r+42))

$\frac{2 r}{r + 6} \div \frac{2 r}{7 r + 42}$

To divide by a fraction, multiply by its reciprocal.

$\frac{2 r}{r + 6} \cdot \frac{7 r + 42}{2 r}$

Cancel the common factor of $2 r$ .

Cancel the common factor.

$\frac{2 r}{r + 6} \cdot \frac{7 r + 42}{2 r}$

Rewrite the expression.

$\frac{1}{r + 6} (7 r + 42)$

Multiply $\frac{1}{r + 6}$ by $7 r + 42$ .

$\frac{7 r + 42}{r + 6}$

Factor $7$ out of $7 r + 42$ .

Factor $7$ out of $7 r$ .

$\frac{7 (r) + 42}{r + 6}$

Factor $7$ out of $42$ .

$\frac{7 r + 7 \cdot 6}{r + 6}$

Factor $7$ out of $7 r + 7 \cdot 6$ .

$\frac{7 (r + 6)}{r + 6}$

Cancel the common factor of $r + 6$ .

Cancel the common factor.

$\frac{7 (r + 6)}{r + 6}$

Divide $7$ by $1$ .

$7$