Giải thích các bước giải:
a.Ta có:
$Q=\dfrac{x\sqrt{x}-1}{x-\sqrt{x}}-\dfrac{x\sqrt{x}+1}{x+\sqrt{x}}+\dfrac{x+1}{\sqrt{x}}$
$\to Q=\dfrac{(\sqrt{x}-1)(x+\sqrt{x}+1)}{\sqrt{x}(\sqrt{x}-1)}-\dfrac{(\sqrt{x}+1)(x-\sqrt{x}+1)}{\sqrt{x}(\sqrt{x}+1)}+\dfrac{x+1}{\sqrt{x}}$
$\to Q=\dfrac{x+\sqrt{x}+1}{\sqrt{x}}-\dfrac{x-\sqrt{x}+1}{\sqrt{x}}+\dfrac{x+1}{\sqrt{x}}$
$\to Q=\dfrac{x+\sqrt{x}+1-(x-\sqrt{x}+1)+x+1}{\sqrt{x}}$
$\to Q=\dfrac{x+2\sqrt{x}+1}{\sqrt{x}}$
b.Ta có $Q=\dfrac{x+2\sqrt{x}+1}{\sqrt{x}}$
$\to Q=\dfrac{(\sqrt{x}+1)^2}{\sqrt{x}}$
$\to Q\ge \dfrac{4\sqrt{x}}{\sqrt{x}}$
$\to Q\ge 4$
