\(A=\frac{2n+3}{n+2}+\frac{3n+7}{n+2}-\frac{5n}{n+2}\)
\(A=\frac{2n+3+3n+7-5n}{n+2}\)
\(A=\frac{5n-5n+10}{n+2}\)
\(A=\frac{10}{n+2}\)
Vì A là số nguyên tố bé nhất.
\(A=\frac{10}{n+2}=2\)
\(10:\left(n+2\right)=2\)
\(n+2=10:2\)
\(n+2=5\)
\(n=5-2\)
Vậy \(n=3\)