$$\frac{3}{4}+\frac{5}{2}[\frac{1}{4}\times(\frac{8}{5}-\frac{4}{3})]$$ is equal to:

$$\ \frac{\ 3}{4}+\ \frac{\ 5}{2}\times\ \left(\frac{\ 1}{4}\times\ \left(\ \frac{\ 8}{5}\ -\ \frac{\ 4}{3}\right)\right)$$

$$=\ \frac{\ 3}{4}+\ \frac{\ 5}{2}\times\ \left(\frac{\ 1}{4}\times\ \left(\frac{\ 24\ -\ 20}{5\times\ 3}\right)\right)$$

$$=\ \frac{\ 3}{4}+\ \frac{\ 5}{2}\times\ \left(\frac{\ 1}{4}\times\ \left(\frac{\ 4}{5\times\ 3}\right)\right)$$

$$=\ \frac{\ 3}{4}+\ \frac{\ 5}{2}\times\ \left(\frac{\ 1}{15}\right)$$

$$=\ \frac{\ 3}{4}+\ \frac{\ 1}{6}$$

$$=\ \frac{\ 9+2}{12}$$

$$=\ \frac{\ 11}{12}.$$

D is correct choice.