\(\frac1{3-\sqrt8}-\frac1{\sqrt8-\sqrt7}+\frac1{\sqrt7-\sqrt6}\)\(-\frac1{\sqrt6-\sqrt5}+\frac1{\sqrt5-2}\)
\(= \frac{3+\sqrt8}{9-8}-\frac{\sqrt8+\sqrt7}{8-7}+\frac{\sqrt7+\sqrt6}{7-6}\)\(-\frac{\sqrt6+\sqrt5}{6-5}+\frac{\sqrt5+2}{5-4}\)
= (3 + √8) - (√8 + √7) + (√7 + √6) - (√6 - √5) + (√5 + 2)
= 3 + 2 = 5
