$$\frac{3^{-2}-{\left({\displaystyle \frac{3}{4}}\right)}^{-2}}{2-{\left({\displaystyle \frac{1}{5}}\right)}^{-1}}$$

$$=\frac{{\displaystyle \frac{1}{3^2}}-{\left({\displaystyle \frac{4}{3}}\right)}^2}{2-{\left({\displaystyle \frac{5}{1}}\right)}^1}$$

$$=\frac{{\displaystyle \frac{1}{9}}-{\displaystyle \frac{16}{9}}}{2-{\displaystyle \frac{5}{1}}}$$

$$=\frac{-{\displaystyle \frac{15}{9}}}{{\displaystyle \frac{4}{2}}-{\displaystyle \frac{10}{2}}}$$

$$=\frac{{\displaystyle -\frac{15}{9}}}{-{\displaystyle \frac{6}{2}}}$$

$$=\frac{{\displaystyle \frac{15}{9}}}{{\displaystyle \frac{6}{2}}}$$

$$=\frac{15·2}{9·6}$$

$$=\frac{30}{54}$$