Question

Simplificati fractia 7^n+2·7^n+1+7^n+2
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2^n+1+2^n+2+2^n+4
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Answer 1

   
[tex]\displaystyle \\ \\ \frac{7^{n} + 2\cdot 7^{n+1}+7^{n+2}}{2^{n+1}+2^{n+2}+2^{n+4}}= \frac{7^{n}(1 + 2\cdot 7^{1}+7^{2})}{2^n(2^{1}+2^{2}+2^{4}}}= \\ \\ = \frac{7^{n}(1 + 14+49)}{2^n(2+4+16)}=\frac{64 \times 7^{n}}{22 \times 2^n}= \frac{2^6 \times 7^{n}}{11 \times 2 \times 2^n}= \\ \\ =\frac{2^6 \times 7^{n}}{11 \times 2^{n+1}}= \frac{2^{6-6} \times 7^{n}}{11 \times 2^{n+1-6}}= \frac{2^{0} \times 7^{n}}{11 \times 2^{n-5}}= \boxed{ \frac{7^{n}}{11 \times 2^{n-5}} } [/tex]