Question

Tìm n thuộc N, để các phân số sau có giá trị là số tự nhiên

a) 3n + 5/ n+1

b) n+13/ n+1

c) 3n +15/ n+1

d) 2n+13/ n-1

e) 3n + 5/ n-2

f) 6n +5/2n+1

Answer 1

a, \(\frac{3n+5}{n+1}=\frac{3\left(n+1\right)+2}{n+1}=\frac{2}{n+1}\)

\(\Rightarrow n+1\in2=\left\{\pm1;\pm2\right\}\)

n + 1	1	-1	2	-2
n	0	-2	1	-3

b, \(\frac{n+13}{n+1}=\frac{n+1+12}{n+1}=\frac{12}{n+1}\)

\(\Rightarrow n+1\inƯ\left(12\right)=\left\{\pm1;\pm2;\pm3;\pm4;\pm6;\pm12\right\}\)

n + 1	1	-1	2	-2	3	-3	4	-4	6	-6	12	-12
n	0	-2	1	-3	2	-4	3	-5	5	-7	11	-13

c, \(\frac{3n+15}{n+1}=\frac{3\left(n+1\right)+12}{n+1}=\frac{12}{n+1}\)

\(\Rightarrow n+1\inƯ\left(12\right)=\left\{\pm1;\pm2;\pm3;\pm4;\pm6;\pm12\right\}\)

n + 1	1	-1	2	-2	3	-3	4	-4	6	-6	12	-12
n	0	-2	1	-3	2	-4	3	-5	5	-7	11	-13