Question
Simplify: $\frac{10\times(5)^{\text{n}+1}+25\times5^{\text{n}}}{3\times(5)^{\text{n}+2}+10\times(5)^{\text{n}+1}}$
✓
Answer
$\frac{10\times(5)^{\text{n}+1}+25\times5^{\text{n}}}{3\times(5)^{\text{n}+2}+10\times(5)^{\text{n}+1}}$
$=\frac{10\times5^{(\text{n}+1)}+5\times5^{(\text{n}+1)}}{3\times5^{(\text{n}+2)}+(2\times5)\times5^{(\text{n}+1)}}$
$=\frac{10\times5^{(\text{n}+1)}+5\times5^{(\text{n}+1)}}{3\times5^{(\text{n}+2)}+(2\times5)\times5^{(\text{n}+1)}}$
$=\frac{5^{(\text{n}+1)}(10+5)}{5^{(\text{n}+1)}(10+15)}$
$=\frac{15}{25}$
$=\frac{3}{5}$
$=\frac{10\times5^{(\text{n}+1)}+5\times5^{(\text{n}+1)}}{3\times5^{(\text{n}+2)}+(2\times5)\times5^{(\text{n}+1)}}$
$=\frac{10\times5^{(\text{n}+1)}+5\times5^{(\text{n}+1)}}{3\times5^{(\text{n}+2)}+(2\times5)\times5^{(\text{n}+1)}}$
$=\frac{5^{(\text{n}+1)}(10+5)}{5^{(\text{n}+1)}(10+15)}$
$=\frac{15}{25}$
$=\frac{3}{5}$
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