Which of the following $u=\sqrt{c+1} - \sqrt{c}$ and $v=\sqrt{c} - \sqrt{c-1}$ is greater? If
$$u=\sqrt{c+1} - \sqrt{c}$$
and 
$$v=\sqrt{c} - \sqrt{c-1}$$
then, which among $u$ and $v$ is greater?
Please help without substituting values.

$u=\frac{(\sqrt{c+1}-\sqrt{c})(\sqrt{c+1}+\sqrt{c})}{\sqrt{c}+\sqrt{c+1}} = \frac{1}{\sqrt{c}+\sqrt{c+1}}$
By analogy.
$v=\frac{1}{\sqrt{c}+\sqrt{c-1}}$.
So,$v>u$
