\(\displaystyle\lim_{{{x}\rightarrow-\infty}}{\frac{{\sqrt{{{3}}}{\left\lbrace{x}\right\rbrace}-{5}{x}+{3}}}{{{2}{x}+{x}^{{{\frac{{{2}}}{{{3}}}}-{4}}}}}}:{\frac{{{x}}}{{{x}}}}=\lim_{{{x}\rightarrow-\infty}}{\frac{{{x}^{{-{\frac{{{2}}}{{{3}}}}-{5}+{\frac{{{3}}}{{{x}}}}}}}}{{{2}+{x}^{{-{\frac{{{1}}}{{{3}}}}-{\frac{{{4}}}{{{x}}}}}}}}}\)=

Use that \(\displaystyle\lim_{{{x}\rightarrow-\infty}}{x}^{{-{n}}}={0}\).

\(\displaystyle={\frac{{{0}-{5}+{0}}}{{{2}+{0}-{0}}}}=-{\frac{{{5}}}{{{2}}}}\)