Question
Simplify the following: $\frac{5\times25^{\text{n}+1}-25\times5^{2\text{n}}}{5\times5^{2\text{n}+3}-(25)^{\text{n}+1}}$
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Answer
$\frac{5\times25^{\text{n}+1}-25\times5^{2\text{n}}}{5\times5^{2\text{n}+3}-(25)^{\text{n}+1}}$ $=\frac{(5\times25^\text{n}\times25)-(25\times25)^\text{n}}{(5\times25^\text{n}\times125)(25)^\text{n}\times25}$ $=\frac{25^\text{n}\times25(5-1)}{25^\text{n}\times25(25-1)}$ $=\frac{4}{24}=\frac{1}{6}$
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