Question

Cho A= n+2/n-5 (n\(\in\)Z; n\(\ne\)5). Tìm n để A\(\in\) Z

Answer 1

n+2 chia hết n-5

n-5 + 7 chia hết n-5

=> n-5 \(\in\) Ư(7)

=> Ư(7)={-1;1;-7;7}

Ta có: 

n-5	-1	1	-7	7
n	4	6	-2	12

Answer 2

\(A=\frac{n+2}{n-5}=\frac{n-5+7}{n-5}=\frac{n-5}{n-5}+\frac{7}{n-5}\in Z\)

=>7 chia hết n-5

=>n-5\(\in\){1,-1,7,-7}

=>n\(\in\){6,4,12,-2}