\(A=\dfrac{11\cdot13\cdot15\left(1+3\cdot3\cdot3+5\cdot5\cdot5+9\cdot9\cdot9\right)}{11\cdot15\cdot17\left(1+3\cdot3\cdot3+5\cdot5\cdot5+9\cdot9\cdot9\right)}\)
\(=\dfrac{11\cdot13\cdot15}{13\cdot15\cdot17}=\dfrac{11}{17}\)
\(B=\dfrac{1111}{1717}=\dfrac{1111:101}{1717:101}=\dfrac{11}{17}\)
=>A=B
\(A=\dfrac{11.13.15+33.39.45+55.65.75+99.117.135}{13.15.17+39.45.51+65.75.85+117.135.153}\)
\(=\dfrac{11.13.15.\left(1+3.3.3+5.5.5+9.9.9\right)}{13.15.17.\left(1+3.3.3+5.5.5+9.9.9\right)}=\dfrac{11}{17}\)
\(B=\dfrac{1111}{1717}=\dfrac{11.101}{17.101}=\dfrac{11}{17}\)
\(=>A=B\)
Có: \(A=\dfrac{11.13.15+33.39.45+55.65.75+99.117.135}{13.15.17+39.45.51+65.75.85+117.135.153}\)(sửa đề)
\(=\dfrac{11.13.15+3^3\left(11.13.15\right)+5^3\left(11.13.15\right)+9^3\left(11.13.15\right)}{13.15.17+3^3\left(13.15.17\right)+5^3\left(13.15.17\right)+9^3\left(13.15.17\right)}\)
\(=\dfrac{11.13.15\left(1+3^3+5^3+9^3\right)}{13.15.17\left(1+3^3+5^3+9^3\right)}\)
\(=\dfrac{11}{17}\)
Có: \(B=\dfrac{1111}{1717}=\dfrac{11.101}{17.101}=\dfrac{11}{17}\)
=> A = B