Answer
$\frac{-10}{(x-5)^{3/2}(x+5)^{1/2} }$
Work Step by Step
$(x-5)^{-1/2}(x+5)^{-1/2}-(x+5)^{1/2}(x-5)^{-3/2}$
This expression can be written as
$=\frac{1}{(x-5)^{1/2}(x+5)^{1/2}} - \frac{(x+5)^{1/2}}{(x-5)^{3/2}}$ Because $[a^{-m/n} =\frac{1}{a^{m/n}} ]$
Take the LCM
$= \frac{(x-5)^{1}-(x+5)^{1/2}.(x+5)^{1/2}}{(x-5)^{3/2}(x+5)^{1/2}}$
$= \frac{(x-5)^{1}-(x+5)^{1/2+1/2}}{(x-5)^{3/2}(x+5)^{1/2}}$ Because $[a^{m}\times a^{n} = a^{m+n}]$
$= \frac{(x-5)-(x+5)}{(x-5)^{3/2}(x+5)^{1/2}}$
Simplify the numerator
$= \frac{(x-5-x-5)}{(x-5)^{3/2}(x+5)^{1/2}}$
$= \frac{(-10)}{(x-5)^{3/2}(x+5)^{1/2}}$
