[tex]a)\ \frac{2^{n+1}\cdot 3^{n-1}}{6^n}=\frac{2^n\cdot 2 \cdot \frac{3^n}{3}}{(2\cdot 3)^n}=\frac{2}{3} \cdot \frac{2^n\cdot 3^n}{2^n \cdot 3^n}=\boxed{\frac{2}{3}}; \\ b) \ \frac{14^n}{2^{n-2}\cdot 7^{n+2}}=\frac{(2\cdot 7)^n}{\frac{2^n}{2^2}\cdot 7^n\cdot 7^2}=\frac{2^n\cdot 7^n}{2^n\cdot 7^n\cdot 49:4}=\boxed{\frac{4}{49} }; \\ c) \ \frac{12^n}{3^{n-1}\cdot 2^{2n+1}}=\frac{(3\cdot 4)^n}{\frac{3^n}{3}\cdot 2^{2n} \cdot 2}=\frac{3^n \cdot 2^{2n}}{3^n\cdot 2^{2n}\cdot 2:3}=\boxed{\frac{3}{2}}.[/tex]
