Tìm số tự nhiên n để 6n+3 chia hết 3n+6.

Đáp án:

Giải thích các bước giải:

Ta có:

$\frac{6n+3}{3n+6}$=$\frac{6n+12-9}{3n+6}$=2-$\frac{9}{3n+6}$

để 6n+3:3n+6

⇔9:3n+6

⇒\(\left[ \begin{array}{l}3n+6=1\\3n+6=-1\end{array} \right.\)

   \(\left[ \begin{array}{l}3n+6=9\\3n+6=-9\end{array} \right.\)

   \(\left[ \begin{array}{l}3n+6=3\\3n+6=-3\end{array} \right.\)

⇒\(\left[ \begin{array}{l}3n=-5\\3n=-7\end{array} \right.\)

   \(\left[ \begin{array}{l}3n=3\\3n=-15\end{array} \right.\)

   \(\left[ \begin{array}{l}3n=-3\\3n=-9\end{array} \right.\)

⇒n=$\frac{-5}{3}$;$\frac{-7}{3}$;1;-5;-1;-3