Answer
$\displaystyle \frac{4x+3}{3(x+1)^{2/3}}$
Work Step by Step
$(x+1)^{1/3}+x\displaystyle \cdot\frac{1}{3}(x+1)^{-2/3}=$
... rewrite the second term moving $(x+1)$ into the denominator
$=(x+1)^{1/3}+\displaystyle \frac{x}{3(x+1)^{2/3}}$
... rewrite, with the first term being a fraction with the common denominator
$=\displaystyle \frac{(x+1)^{1/3}\cdot 3(x+1)^{2/3}+x}{3(x+1)^{2/3}}$
... apply $a^{m}\cdot a^{n}=a^{m+n}$ to the first term of the numerator
$=\displaystyle \frac{3(x+1)^{1/3+2/3}+x}{3(x+1)^{2/3}}$
$=\displaystyle \frac{3(x+1)^{1}+x}{3(x+1)^{2/3}}$
$=\displaystyle \frac{3x+3+x}{3(x+1)^{2/3}}$
$=\displaystyle \frac{4x+3}{3(x+1)^{2/3}}$
