Question

Answer 1

Bài 1:

-Đặt ƯCLN(3n+1,4n+1)=a (a∈N*)

-Có: \(\left(3n+1\right)⋮a;\left(4n+1\right)⋮a\)

\(\Rightarrow\left(12n+4\right)⋮a;\left(12n+3\right)⋮a\)

\(\Rightarrow\left[\left(12n+4\right)-\left(12n+3\right)\right]⋮a\)

\(\Rightarrow1⋮a\)

\(\Rightarrow a=1\)

-Vậy phân số \(\dfrac{3n+1}{4n+1}\) tối giản với mọi n∈Z

Answer 2

-Đặt ƯCLN(3n+1,4n+1)=a (a∈N*)

-Có: (3n+1)⋮a;(4n+1)⋮a(3n+1)⋮a;(4n+1)⋮a

⇒(12n+4)⋮a;(12n+3)⋮a⇒(12n+4)⋮a;(12n+3)⋮a

⇒[(12n+4)−(12n+3)]⋮a⇒[(12n+4)−(12n+3)]⋮a

⇒1⋮a⇒1⋮a

-Vậy phân số