Question

[Dream_Fake [ Team Noob ]+(ᴳᵒᵈ乡T̸͟͞...]

Tìm \(n\in Z\) để \(A=\frac{n+1}{n-2}\left(n\ne2\right)\)có giá trị nguyên

Mn giúp mik vs, đúng thì mik k cho

Answer 1

[Đoàn Đức Hà]

\(A=\frac{n+1}{n-2}=\frac{n-2+3}{n-2}=1+\frac{3}{n-2}\inℤ\Leftrightarrow\frac{3}{n-2}\inℤ\)

mà \(n\inℤ\)nên \(n-2\inƯ\left(3\right)=\left\{-3,-1,1,3\right\}\)

\(\Leftrightarrow n\in\left\{-1,1,3,5\right\}\).