Biến đổi vế trái ta có:
$\dfrac{\sqrt a + \sqrt b}{2\sqrt a - 2\sqrt b} - \dfrac{\sqrt a - \sqrt b}{2\sqrt a + 2\sqrt b} - \dfrac{2b}{b- a} (a \neq b; a\geq 0 ; b \geq 0)$
$=\dfrac{\sqrt a + \sqrt b}{2(\sqrt a- \sqrt b)} - \dfrac{\sqrt a- \sqrt b}{2(\sqrt a + \sqrt b)} - \dfrac{2b}{(\sqrt a + \sqrt b)(\sqrt b - \sqrt a)}$
$=\dfrac{\sqrt a + \sqrt b}{2(\sqrt a- \sqrt b)} - \dfrac{\sqrt a- \sqrt b}{2(\sqrt a + \sqrt b)} + \dfrac{2b}{(\sqrt a + \sqrt b)(\sqrt a - \sqrt b)}$
$=\dfrac{(\sqrt a + \sqrt b)^2 - (\sqrt a - \sqrt b)^2 + 4b}{2((\sqrt a + \sqrt b)(\sqrt a - \sqrt b)}$
$=\dfrac{a + 2\sqrt{ab} + b - a + 2\sqrt{ab} - b + 4b}{2((\sqrt a + \sqrt b)(\sqrt a - \sqrt b)}$
$=\dfrac{4\sqrt{ab} + 4b}{2((\sqrt a + \sqrt b)(\sqrt a - \sqrt b)}$
$=\dfrac{4\sqrt b(\sqrt a + \sqrt b)}{2((\sqrt a + \sqrt b)(\sqrt a - \sqrt b)}$
$=\dfrac{2\sqrt b}{\sqrt a - \sqrt b} = VP$
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