Question

Determinati n∈N pentru care exista (au sens) fractiile :
a)   1 supra n
b)  7 supra n-3
c) (3 supra n-4)
D) 2 supra n + 3 

Answer 1

$O \ fractie \ de \ forma \ \frac{a}{b} \ are \ sens \ daca \ b \neq 0\\ \\a) \ \frac{1}{n} \ are \ sens \ oricare \ ar \ fi \ n \in \mathbb{N^*}\\ \\ b) \ \frac{7}{n-3} \ are \ sens \ oricare \ ar \ fi \ n \in \mathbb{N}-\{3\}, \ (n-3\neq 0 \Rightarrow n \neq 3)\\ \\ c) \ \frac{3}{n-4}\ are \ sens \ pentru \ n-4\neq 0 \Rightarrow n \neq 4, \ deci \ oricare \ ar \ fi \ n\in \mathbb{N}-\{4\}\\ \\ d) \ \frac{2}{n+3} \ are \ sens \ oricare \ ar \ fi \ n+3 \neq 0 \Rightarrow n\neq-3 \Rightarrow are \ sens \ pentru \ orice \ n \in \mathbb{N}$