( 32/3 )^2 - ( 21/2 )^2 ( 43/4 )^2 - ( 31/3 )^2 ÷ 32/3 - 21/243/4 - 31/3 = ?

Answer: Option B

$$\begin{array}{rl}& \text{If }a=3\frac{2}{3},\\ & b=2\frac{1}{2},\\ & c=4\frac{3}{4},\\ & d=3\frac{1}{3},\\ & \text{then}\\ & \text{Given expression ,}\\ & \frac{\left(a^2-b^2\right)}{\left(c^2-d^2\right)}÷\frac{\left(a-b\right)}{\left(c-d\right)}\\ & =\frac{\left(a^2-b^2\right)}{\left(c^2-d^2\right)}\times \frac{\left(c-d\right)}{\left(a-b\right)}\\ & =\frac{\left(a+b\right)}{\left(c+d\right)}\\ & =\frac{3\frac{2}{3}+2\frac{1}{2}}{4\frac{3}{4}+3\frac{1}{3}}\\ & =\frac{\frac{11}{3}+\frac{5}{2}}{\frac{19}{4}+\frac{10}{3}}\\ & =\frac{37}{6}\times \frac{12}{97}\\ & =\frac{74}{97}\end{array}$$