Answer
$\frac{x+4}{(x+5)^{3/2}}$
Work Step by Step
$(x+5)^{-1/2}-(x+5)^{-3/2}$
The greatest common factor of $(x+5)^{-1/2}-(x+5)^{-3/2}$ is $(x+5)$ with the smaller exponent in the two terms. Thus the greatest common factor is $(x+5)^{-3/2}$
Express each term as the product of greatest common factor and its other factor.
$=(x+5)^{1}(x+5)^{-3/2}-(x+5)^{-3/2}$
$[(x+5)^{1}(x+5)^{-3/2}=(x+5)^{-3/2+1}=(x+5)^{-1/2}]$
Factor out the Greatest common factor.
$=(x+5)^{-3/2}((x+5)-1)$
$=(x+5)^{-3/2}(x+5-1)$
$=(x+5)^{-3/2}(x+4)$
$=\frac{(x+4)}{(x+5)^{3/2}}$ $[a^{-1/m} = \frac{1}{a^{1/m}}]$
