$f(x)=\frac{{{x}^{3}}}{3{{x}^{2}}-2}-\frac{{{x}^{2}}}{3x-1}=\frac{{{x}^{3}}(3x-1)-{{x}^{2}}(3{{x}^{2}}-2)}{(3{{x}^{2}}-2)(3x-1)}=\frac{(3{{x}^{4}}-{{x}^{3}})-(3{{x}^{4}}-{{x}^{2}})}{9{{x}^{3}}-3{{x}^{2}}-6x+2}$ $\Rightarrow f(x)=\frac{-{{x}^{3}}+2{{x}^{2}}}{9{{x}^{3}}-3{{x}^{2}}-6x+2}\Rightarrow \underset{x\to -\infty }{\mathop{\lim }}\,f(x)=\underset{x\to -\infty }{\mathop{\lim }}\,\frac{-{{x}^{3}}}{9{{x}^{3}}}=-\frac{1}{9}$