M = `(\sqrt{x}-3)/(\sqrt{x}+2)` tìm x để M nguyên

`\frac{\sqrt{x} - 3}{\sqrt{x} + 2}` `<=>` `\frac{\sqrt{x} + 2 - 5}{\sqrt{x} + 2}`

`<=>` `\frac{\sqrt{x + 2}}{\sqrt{x + 2}}` `+` `\frac{-5}{\sqrt{x + 2} }` `<=> 1 +` `\frac{-5}{\sqrt{x} + 2}`

 Để `M` ∈ số nguyên

`=> -5` ⋮ $\sqrt{x + 2}$ 

`@`$\sqrt{x + 2}$ `= 5`

`<=>` $\sqrt{x}$ `= 3`

`<=> x = 9 ( N )`

`@` $\sqrt{x + 2}$ `= -5`

`<=>` $\sqrt{x}$ `= -7`

`<=> x = - 49 ( L )`

`@` $\sqrt{x + 2}$ `= 1`

`<=>` $\sqrt{x}$ `= -1`

`<=> x = - 1 ( L )`

`@` $\sqrt{x + 2}$ `= -1`

`<=>` $\sqrt{x}$ `= -3`

`<=> x = -9 ( L )`

Vậy `x ∈ { 9 }`