\(\frac{2x+15}{x+1}=\frac{2\left(x+1\right)+13}{x+1}=\frac{2\left(x+1\right)}{x+1}+\frac{13}{x+1}=2+\frac{13}{x+1}\)
Để \(2+\frac{3}{x+1}\in Z\Leftrightarrow\frac{3}{x+1}\in Z\)
=> x + 1 ∈ Ư ( 3 ) = { - 3 ; - 1 ; 1 ; 3 }
=> x ∈ { - 4 ; - 2 ; 0 ; 2 }
$\frac{2x+15}{x+1}=\frac{2\left(x+1\right)+13}{x+1}=\frac{2\left(x+1\right)}{x+1}+\frac{13}{x+1}=2+\frac{13}{x+1}$2x+15x+1 =2(x+1)+13x+1 =2(x+1)x+1 +13x+1 =2+13x+1
Để $2+\frac{3}{x+1}\in Z\Leftrightarrow\frac{3}{x+1}\in Z$
Trả lời: \(\frac{2x+15}{x+1}=2+\frac{13}{x+1}\)
nên x+1 là Ư(13) và x=0;-2;12;-14