By rule of the domain of the function that denominator can not be zero, we have \(\displaystyle{\left({x}^{{3}}\right)}+{\left({x}^{{2}}\right)}≠{0}\)

\(\displaystyle{\left({x}^{{3}}\right)}+{\left({x}^{{2}}\right)}={\left({x}^{{2}}\right)}{\left({x}+{1}\right)},\) that is xero for \(\displaystyle{x}^{{2}}={0}\), viz \(x=0\) and \(x+1=0, viz\ x=-1\).

So, we conclude, the domain of the given function is \(\displaystyle{R}{\left\lbrace{\left(-{1.0}\right\rbrace}\right.}\)