$$\frac{x^{-5}+2x^2-x}{x^{-3}}$$

$$=\frac{{\displaystyle \frac{1}{x^5}}+2x^2-x}{{\displaystyle \frac{1}{x^3}}}$$

$$=\frac{{\displaystyle \frac{1}{x^5}}+2x^2·{\displaystyle \frac{x^5}{x^5}}-x·{\displaystyle \frac{x^5}{x^5}}}{{\displaystyle \frac{1}{x^3}}}$$

$$=\frac{{\displaystyle \frac{1}{x^5}}+{\displaystyle \frac{2x^7}{x^5}}-{\displaystyle \frac{x^6}{x^5}}}{{\displaystyle \frac{1}{x^3}}}$$

$$=\frac{{\displaystyle \frac{1+2x^7-x^6}{x^5}}}{{\displaystyle \frac{1}{x^3}}}$$

$$=\frac{1+2x^7-x^6}{x^5}÷\frac{1}{x^3}$$

$$=\frac{1+2x^7-x^6}{\cancel{x^5}}·\frac{\cancel{x^3}}{1}$$

$$=\frac{1+2x^7-x^6}{x^2}$$