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Điều kiện $x \ge 1/2$. BPT
$\Leftrightarrow \sqrt{2x-1}-1+\sqrt{x+3}-2+x^{2}+x-2>0$
$\Leftrightarrow \dfrac{2(x-1)}{\sqrt{2x-1}+1}+\dfrac{x-1}{\sqrt{x+3}+2}+(x-1)(x+2)>0$
$\Leftrightarrow (x-1)\left ( \dfrac{2}{\sqrt{2x-1}+1}+\dfrac{1}{\sqrt{x+3}+2}+(x+2) \right )>0$
Dễ thấy $\dfrac{2}{\sqrt{2x-1}+1}+\dfrac{1}{\sqrt{x+3}+2}+(x+2)>0$.
Vậy BPT $\Leftrightarrow x>1.$
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