Chapter P, Prerequisites - Section P.7 - Rational Expressions - P.7 Exercises - Page 52: 84

$\frac{7-\frac{3}{2}x}{(7-3x)^{3/2}}$

We factor out $(7-3x)^{-1/2}$, remembering that $(7-3x)^{-1/2}*(7-3x)=(7-3x)^{1/2}$: $\displaystyle \frac{(7-3x)^{1/2}+\frac{3}{2}x(7-3x)^{-1/2}}{7-3x}=\frac{(7-3x)^{-1/2}(7-3x+\frac{3}{2}x)}{7-3x}=\frac{7-\frac{3}{2}x}{(7-3x)^{3/2}}$