Question

cho n+3/n+2 tìm n thuộc Z sao cho n+3/n+2 là số nguyên

Answer 1

Để \(\frac{n+3}{n+2}=\frac{n+2+1}{n+2}=1+\frac{1}{n+2}\in Z\)

\(\Leftrightarrow\frac{1}{n+2}\in Z\Leftrightarrow n+2\inƯ\left(1\right)\Leftrightarrow n+2\in\left\{-1;1\right\}\Leftrightarrow n\in\left\{-3;-1\right\}\)

Answer 2

để \(\frac{n+3}{n+2}\in Z\Rightarrow\)n+3 chia hết cho n+2

=>(n+2)+1 chia hết cho n+2

=>1 chia hết n+2

\(\Rightarrow n+2\in\left\{-1;1\right\}\)

\(\Rightarrow n\in\left\{-3;-1\right\}\)

vậy n=-3;-1