The simplest value of ( 1 9 - 8 - 1 8 - 7 + 1 7 - 6 - 1 6 - 5 ) is = ?

Answer: Option A

$$\left(\frac{1}{\sqrt{9}-\sqrt{8}}-\frac{1}{\sqrt{8}-\sqrt{7}}+\frac{1}{\sqrt{7}-\sqrt{6}}-\frac{1}{\sqrt{6}-\sqrt{5}}\right)$$
$$\begin{array}{rl}& =\sqrt{9}+\sqrt{8}-\sqrt{8}-\sqrt{7}+\sqrt{7}+\sqrt{6}-\sqrt{6}-\sqrt{5}\\ & =\sqrt{9}-\sqrt{5}\\ & =3-\sqrt{5}\end{array}$$