Answer
$\displaystyle \frac{7}{9}$
Work Step by Step
Dividing with $\displaystyle \frac{P}{Q}$ equals multiplying with the reciprocal, $\displaystyle \frac{Q}{P}.$
$\displaystyle \frac{x+1}{3}\div\frac{3x+3}{7}=\frac{x+1}{3}\cdot\frac{7}{3x+3}\qquad$... factor what you can
$=\displaystyle \frac{x+1}{3}\cdot\frac{7}{3(x+1)}\qquad$... divide out the common factors
$=\displaystyle \frac{1}{3}\cdot\frac{7}{3(1)}\qquad$
= $\displaystyle \frac{7}{9}$
