Giải thích các bước giải:
ĐKXĐ: $a, b\ge 0, a\ne b$
Ta có:
$A=\dfrac{a\sqrt{a}-1}{\sqrt{a}-1}\cdot (\dfrac{\sqrt{a}}{\sqrt{a}-\sqrt{b}}-\dfrac{\sqrt{b}}{\sqrt{a}+\sqrt{b}}+\dfrac{2b}{b-a})$
$\to A=\dfrac{(\sqrt{a}-1)(a+\sqrt{a}+1)}{\sqrt{a}-1}\cdot (\dfrac{\sqrt{a}(\sqrt{a}+\sqrt{b})-\sqrt{b}(\sqrt{a}-\sqrt{b})}{(\sqrt{a}-\sqrt{b})(\sqrt{a}+\sqrt{b})}-\dfrac{2b}{a-b})$
$\to A=(a+\sqrt{a}+1)\cdot (\dfrac{a+\sqrt{ab}-\sqrt{ab}+b}{a-b}-\dfrac{2b}{a-b})$
$\to A=(a+\sqrt{a}+1)\cdot (\dfrac{a+b}{a-b}-\dfrac{2b}{a-b})$
$\to A=(a+\sqrt{a}+1)\cdot \dfrac{a+b-2b}{a-b}$
$\to A=(a+\sqrt{a}+1)\cdot \dfrac{a-b}{a-b}$
$\to A=(a+\sqrt{a}+1)\cdot 1$
$\to A=a+\sqrt{a}+1$