Question

tìm n:

a, n+6 chia hết n+2

b,2n+3 chia hết n - 2

c,3n+1 chia hết 11 -2n

Answer 1

a) \(\frac{n+6}{n+2}=\frac{n+2+4}{n+2}=\frac{n+2}{n+2}+\frac{4}{n+2}=1+\frac{4}{n+2}\)

Mà \(1\in Z\Rightarrow4⋮n+2\Rightarrow n+2\inƯ\left(4\right)\Rightarrow n+2\in\left\{-4;-2;-1;1;2;4\right\}\)

\(\Rightarrow n\in\left\{-6;-4;-3;-1;0;2\right\}\)

b)\(\frac{2n+3}{n-2}=\frac{2n-4+7}{n-2}=\frac{2.\left(n-2\right)}{n-2}+\frac{7}{n-2}=2+\frac{7}{n-2}\)

Mà \(2\in Z\Rightarrow n-2\inƯ\left(7\right)\Rightarrow n-2\in\left\{-7;-1;1;7\right\}\Rightarrow n\in\left\{-5;1;3;9\right\}\)