The simplified form of
$\frac{1}{\sqrt{3}+\sqrt{4}}+\frac{1}{\sqrt{4}+\sqrt{5}}+\frac{1}{\sqrt{5}+\sqrt{6}}+\frac{1}{\sqrt{6}+\sqrt{7}}+\frac{1}{\sqrt{7}+\sqrt{8}}+\frac{1}{\sqrt{8}+\sqrt{9}}$ is :
[A]$\sqrt{3}$
[B]$3-\sqrt{3}$
[C]$3\sqrt{3}$
[D]$5-\sqrt{3}$

$\mathbf{3-\sqrt{3}}$
$\frac{1}{\sqrt{3}+\sqrt{4}}$
$= \frac{1}{\sqrt{3}+\sqrt{4}}\times \frac{\sqrt{4}-\sqrt{3}}{\sqrt{4}-\sqrt{3}}$
$= \frac{\sqrt{4}-\sqrt{3}}{4-3} = \sqrt{4}-\sqrt{3}$
$similarly,\ \frac{1}{\sqrt{4}+\sqrt{5}} = \sqrt{5}-\sqrt{4}\ ......\ so\ on.$
∴ Expression =
$= \sqrt{4}-\sqrt{3}+\sqrt{5}-\sqrt{4}+\sqrt{6}-\sqrt{5}+\sqrt{7}-\sqrt{6}+\sqrt{8}-\sqrt{7}+\sqrt{9}-\sqrt{8} = \sqrt{9}-\sqrt{3} = 3-\sqrt{3}$
Hence option [B] is correct answer.