Question

Simplify :
$\bold{ \frac{10 \times {5}^{n + 1} + 25 \times {5}^{n} }{3 \times {5}^{n + 2} + 10 \times {5}^{n + 1} } }$

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Answer 1

$\huge \underline\bold\color{red}{†SolutioN†}$

$\color{black}\bold</p><p>{ \frac{10 \times {5}^{n + 1} + 25 \times {5}^{n} }{3 \times {5}^{n + 2} + 2 \times {5}^{n + 2} } }$

$\color{black}\bold</p><p>{ = \frac{2 \times 5 \times {5}^{n + 1} + {5}^{2} \times {5}^{n} }{3 \times {5}^{n + 2} + 2 \times 5 \times {5}^{n + 1} } }$

$\color{black}\bold</p><p>{ = \frac{ {2 \times 5}^{n + 1 + 1} + {5}^{n + 2} }{3 \times {5}^{n + 2} + 2 \times {5}^{n + 1 + 1} } }$

$\color{black}\bold</p><p>{ = \frac{2 \times {5}^{n + 2} + {5}^{n + 2} }{3 \times {5}^{n + 2} + 2 \times {5}^{n + 2} } }$

$\color{black}\bold</p><p>{ = \frac{ {5}^{n + 2}(2 + 1) }{ {5}^{n + 2} (3 + 2)} }$

$\color{black}\bold</p><p>{ = \frac{2 + 1}{3 + 2} }$

$\color{black}\bold</p><p>{ = \frac{3}{5} }$

${ \boxed{∵ \: require d \: ans = \frac{3}{5} }}</p><p>$