Question

Aratati ca fractia 2n+7/n+3 este ireductibila

Answer 1

According to Euclidean's algorithm:

GCD(a, b) = GCD(a-b, b), a > b

GCD(a, b) = GCD(a, b-a), b > a

GCD(2n+7, n+3) = GCD(2n+7-n-3, n+3) = GCD(n+4, n+3) =

= GCD(n+4-n-3, n+3) = GCD(1, n+3) = 1

⇒ The fraction is irreductible.

Answer 2

I'm not sure with it.