Given $$\mathop y\limits^{..} \left( t \right) + 3\mathop y\limits^. \left( t \right) + 4y\left( t \right) = 2\mathop x\limits^{..} \left( t \right) + 7\mathop x\limits^. \left( t \right) + 8x\left( t \right)$$
Then H(s) is given by

A. $$H\left( s \right) = \frac{{{s^2} + 3s + 4}}{{2{s^2} + 7s + 8}}$$

B. $$H\left( s \right) = \frac{{2{s^2} + 7s + 8}}{{{s^2} + 3s + 4}}$$

C. $$H\left( s \right) = \frac{{{s^2} + 7s + 8}}{{2{s^2} + 3s + 4}}$$

D. $$H\left( s \right) = \frac{{{s^2} + 8s + 7}}{{2{s^2} + 3s + 4}}$$

Answer: Option B