Question

hãy rút gọn

\(\dfrac{1+3^4+3^8+3^{12}}{1+3^2+3^4+3^6+3^8+3^{10}+3^{12}}\)

Answer 1

Lời giải:

\(\frac{1+3^4+3^8+3^{12}}{1+3^2+3^4+3^6+3^8+3^{10}+3^{12}+3^{14}}=\frac{1+3^4+3^8+3^{12}}{(1+3^4+3^8+3^{12})+(3^2+3^6+3^{10}+3^{14})}\)

\(=\frac{1+3^4+3^8+3^{12}}{(1+3^4+3^8+3^{12})+3^2(1+3^4+3^{8}+3^{12})}\)

\(=\frac{1+3^4+3^8+3^{12}}{(1+3^2)(1+3^4+3^8+3^{12})}=\frac{1}{1+3^2}=\frac{1}{10}\)

Answer 2

Lời giải:

\(\frac{1+3^4+3^8+3^{12}}{1+3^2+3^4+3^6+3^8+3^{10}+3^{12}+3^{14}}=\frac{1+3^4+3^8+3^{12}}{(1+3^4+3^8+3^{12})+(3^2+3^6+3^{10}+3^{14})}\)

\(=\frac{1+3^4+3^8+3^{12}}{(1+3^4+3^8+3^{12})+3^2(1+3^4+3^{8}+3^{12})}\)

\(=\frac{1+3^4+3^8+3^{12}}{(1+3^2)(1+3^4+3^8+3^{12})}=\frac{1}{1+3^2}=\frac{1}{10}\)