a) Gọi \(d\)là \(ƯC\left(n+4;n+3\right)\)\(\left(d\ne0;d\in Z\right)\)
\(\Rightarrow n+4⋮d;n+3⋮d\)
\(\Rightarrow n+4-n+3⋮d\)
\(\Rightarrow1⋮d\Rightarrow d=1\)
Vậy \(\frac{n+4}{n+3}\)là phân số tối giản.
b) Gọi \(d\)là \(ƯC\left(2n+1;n+1\right)\)
\(\Rightarrow2n+1⋮d;n+1⋮d\)
\(\Rightarrow2n+1⋮d;2\left(n+1\right)⋮d\)
\(hay\)\(2n+1⋮d;2n+2⋮d\)
\(\Rightarrow2n+2-2n+1\)\(⋮\)\(d\)
\(\Rightarrow1⋮d\Rightarrow d=1\)
Vậy \(\frac{2n+1}{n+1}\)là phân số tối giản.