Answer:
\[\frac{10\times {{5}^{n+1}}+25\times {{5}^{n}}}{3\times {{5}^{n+2}}+10\times {{5}^{n+1}}}\] \[=\frac{2\times 5\times {{5}^{n}}\times {{5}^{1}}+5\times 5\times {{5}^{n}}}{3\times {{5}^{n}}\times {{5}^{2}}+2\times 5\times {{5}^{1}}\times {{5}^{n}}}\] \[=\frac{2\times 5\times {{5}^{n}}\times 5+5\times 5\times {{5}^{n}}}{3\times {{5}^{n}}\times 5+2\times 5\times 5\times {{5}^{n}}}\] \[=\frac{5\times 5\times {{5}^{n}}(2+1)}{5\times 5\times {{5}^{n}}(3+2)}=\frac{\left( 2+1 \right)}{\left( 3+2 \right)}\] \[=\frac{3}{2}\]
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