Question

Aratati ca urmatoarele fractii sunt ireductibile :
n+3/n+2
n+1/2n+1

Answer 1

n+3/n+2

Consideram ca exista d astfel incat

d|(n+3) si d|(n+2)

=> d|[(n+3)-(n+2)] => d|(n+3-n-2) => d|1

=> fractia nu poate fi reductibila, e ireductibila

n+1/2n+1

Presupunem ca fractia e reductibila, asadar exista d astfel incat

d|(n+1) si d|(2n+1)

d|(n+1) => d|(2n+2)

=> d| [(2n+2)-(2n+1)] => d| (2n+2-2n-1)

=> d|1 => fractia e ireductibila

Semnat M.I.A.