The third term from the end in the expansion of  ${(\frac{3x}{5}-\frac{5}{2x})}^8$ is

The third term from the end in the expansion of  ${\left(\frac{3x}{5}-\frac{5}{2x}\right)}^8$ is

$p=3,n=8$

$T_{n-p+2}=T_{8-3+2}=T_7$

$T_7=T_{6+1}=8_{c_6}{\left(\frac{3x}{5}\right)}^2{(-\frac{5}{2x})}^6$

$=28\frac{9.x^2}{25}.\frac{5^6}{2^6.x^6}$

$=\frac{{\mathrm{28.9.5}}^6}{{25.2}^2{.2}^4{x}^4}=\frac{{\mathrm{7.9.5}}^4}{2^4.x^4}=\frac{39375}{16x^4}$