Answer
$\dfrac{(7-3x)^{1/2}+\frac{3}{2}x(7-3x)^{-1/2}}{7-3x}=\dfrac{3x-14}{2(3x-7)\sqrt{7-3x}}$
Work Step by Step
$\dfrac{(7-3x)^{1/2}+\frac{3}{2}x(7-3x)^{-1/2}}{7-3x}$
Take out common factor $(7-3x)^{-1/2}$ from the numerator:
$\dfrac{(7-3x)^{1/2}+\frac{3}{2}x(7-3x)^{-1/2}}{7-3x}=...$
$...=\dfrac{(7-3x)^{-1/2}[(7-3x)+\frac{3}{2}x]}{7-3x}=...$
Simplify the expression inside brackets:
$...=\dfrac{(7-3x)^{-1/2}\Big(7-3x+\dfrac{3}{2}x\Big)}{7-3x}=\dfrac{(7-3x)^{-1/2}\Big(7-\dfrac{3}{2}x\Big)}{7-3x}=...$
Simplify the rational expression:
$...=(7-3x)^{-3/2}\Big(7-\dfrac{3}{2}x\Big)=\dfrac{7-\dfrac{3}{2}x}{(7-3x)^{3/2}}=\dfrac{14-3x}{2(7-3x)^{3/2}}=...$
$...=\dfrac{14-3x}{2\sqrt{(7-3x)^{3}}}=\dfrac{14-3x}{2(7-3x)\sqrt{7-3x}}=\dfrac{3x-14}{2(3x-7)\sqrt{7-3x}}$
