Answer
$(x^{2}+3)^{-1/3}-\dfrac{2}{3}x^{2}(x^{2}+3)^{-4/3}=\dfrac{x^{2}+9}{3(x^{2}+3)\sqrt[4]{x^{2}+3}}$
Work Step by Step
$(x^{2}+3)^{-1/3}-\dfrac{2}{3}x^{2}(x^{2}+3)^{-4/3}$
Take out common factor $(x^{2}+3)^{-4/3}$:
$(x^{2}+3)^{-1/3}-\dfrac{2}{3}x^{2}(x^{2}+3)^{-4/3}=...$
$...=(x^{2}+3)^{-4/3}[(x^{2}+3)-\dfrac{2}{3}x^{2}]=...$
Simplify the expression inside brackets:
$...=(x^{2}+3)^{-4/3}\Big[\dfrac{1}{3}x^{2}+3\Big]=...$
Rearrange:
$...=\dfrac{\dfrac{1}{3}x^{2}+3}{(x^{2}+3)^{4/3}}=\dfrac{x^{2}+9}{3(x^{2}+3)^{4/3}}=\dfrac{x^{2}+9}{3\sqrt[3]{(x^{2}+3)^{4}}}=...$
$...=\dfrac{x^{2}+9}{3(x^{2}+3)\sqrt[4]{x^{2}+3}}$
