$$\frac{16a^{6}b^{7}}{4\left(5a^{2}+3b\right)a^{3}b^{4}}$$

$$\frac{4a^{3}b^{3}}{5a^{2}+3b}$$

$$\frac{\left(12b^{5}a^{3}+20b^{4}a^{5}\right)\frac{\mathrm{d}}{\mathrm{d}a}(16b^{7}a^{6})-16b^{7}a^{6}\frac{\mathrm{d}}{\mathrm{d}a}(12b^{5}a^{3}+20b^{4}a^{5})}{\left(12b^{5}a^{3}+20b^{4}a^{5}\right)^{2}}$$

$$\frac{\left(12b^{5}a^{3}+20b^{4}a^{5}\right)\times 6\times 16b^{7}a^{6-1}-16b^{7}a^{6}\left(3\times 12b^{5}a^{3-1}+5\times 20b^{4}a^{5-1}\right)}{\left(12b^{5}a^{3}+20b^{4}a^{5}\right)^{2}}$$

$$\frac{\left(12b^{5}a^{3}+20b^{4}a^{5}\right)\times 96b^{7}a^{5}-16b^{7}a^{6}\left(36b^{5}a^{2}+100b^{4}a^{4}\right)}{\left(12b^{5}a^{3}+20b^{4}a^{5}\right)^{2}}$$

$$\frac{12b^{5}a^{3}\times 96b^{7}a^{5}+20b^{4}a^{5}\times 96b^{7}a^{5}-16b^{7}a^{6}\left(36b^{5}a^{2}+100b^{4}a^{4}\right)}{\left(12b^{5}a^{3}+20b^{4}a^{5}\right)^{2}}$$

$$\frac{12b^{5}a^{3}\times 96b^{7}a^{5}+20b^{4}a^{5}\times 96b^{7}a^{5}-\left(16b^{7}a^{6}\times 36b^{5}a^{2}+16b^{7}a^{6}\times 100b^{4}a^{4}\right)}{\left(12b^{5}a^{3}+20b^{4}a^{5}\right)^{2}}$$

$$\frac{12b^{5}\times 96b^{7}a^{3+5}+20b^{4}\times 96b^{7}a^{5+5}-\left(16b^{7}\times 36b^{5}a^{6+2}+16b^{7}\times 100b^{4}a^{6+4}\right)}{\left(12b^{5}a^{3}+20b^{4}a^{5}\right)^{2}}$$

$$\frac{1152b^{12}a^{8}+1920b^{11}a^{10}-\left(576b^{12}a^{8}+1600b^{11}a^{10}\right)}{\left(12b^{5}a^{3}+20b^{4}a^{5}\right)^{2}}$$

$$\frac{576b^{12}a^{8}+320b^{11}a^{10}}{\left(12b^{5}a^{3}+20b^{4}a^{5}\right)^{2}}$$