[toan] x nguyên a nguyên

P

phamhuy20011801

$\dfrac{x-\sqrt{x}-12}{x+\sqrt{x}-6}\\
=\dfrac{(\sqrt{x}+3)(\sqrt{x}-4)}{(\sqrt{x}+3)(\sqrt{x}-2)}\\
=\dfrac{\sqrt{x}-4}{\sqrt{x}-2}\\
=\dfrac{\sqrt{x}-2}{\sqrt{x}-2}-\dfrac{2}{\sqrt{x}-2}\\
=1-\dfrac{2}{\sqrt{x}-2}$

Để biểu thức nguyên cần có $\dfrac{2}{\sqrt{x}-2}$ nguyên.
$\rightarrow \sqrt{x}-2 \in Ư(2)$
 
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