Answer
${({x^{2}}+1)^{-3}}+\frac{3}{4}{({x^{2}}+1)^{-\frac{1}{3}}}$
Work Step by Step
$\frac{1}{({x^{2}}+1)^{3}}-\frac{3}{4\sqrt[3] (x^{2}+1)}=\frac{1}{({x^{2}}+1)^{3}}-\frac{3}{4(x^{2}+1)^{\frac{1}{3}}}={({x^{2}}+1)^{-3}}+\frac{3}{4}\times\frac{1}{{({x^{2}}+1)^{\frac{1}{3}}}}={({x^{2}}+1)^{-3}}+\frac{3}{4}{({x^{2}}+1)^{-\frac{1}{3}}}$
