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