Question

\(\dfrac{5-\dfrac{5}{3}-\dfrac{5}{9}-\dfrac{5}{27}}{8-\dfrac{8}{3}-\dfrac{8}{9}-\dfrac{8}{27}}\)chia\(\dfrac{15-\dfrac{15}{11}+\dfrac{15}{121}}{16-\dfrac{16}{11}+\dfrac{15}{121}}\)

Answer 1

Đặt:

`A = (5 - 5/3 - 5/9 - 5/27)/(8 - 8/3 - 8/9 - 8/27) `

`= (5.(1 - 1/3 - 1/9 - 1/27))/(8.(1 - 1/3 -1/9 - 1/27) )`

`= 5/8`

`B = (15 - 15/11 + 15/121)/(16 - 16/11 + 16/121) `

`= (15 . (1 - 1/11 + 1/121))/(16.(1 - 1/11 + 1/121))`

`= 15/16`

Biểu thức `= A  : B = 5/8 : 15/16 = 2/3`

Answer 2

\(\dfrac{5-\dfrac{5}{3}-\dfrac{5}{9}-\dfrac{5}{27}}{8-\dfrac{8}{3}-\dfrac{8}{9}-\dfrac{8}{27}}:\dfrac{15-\dfrac{15}{11}+\dfrac{15}{121}}{16-\dfrac{16}{11}+\dfrac{15}{121}}\)
\(=\dfrac{5.\left(1-\dfrac{1}{3}-\dfrac{1}{9}-\dfrac{1}{27}\right)}{8.\left(1-\dfrac{1}{3}-\dfrac{1}{9}-\dfrac{1}{27}\right)}:\dfrac{15.\left(1-\dfrac{1}{11}+\dfrac{1}{121}\right)}{16.\left(1-\dfrac{16}{11}+\dfrac{15}{121}\right)}\)
\(=\dfrac{5}{8}:\dfrac{15}{16}\)
\(=\dfrac{5}{8}.\dfrac{16}{15}\)
\(=\dfrac{1.2}{1.3}\)
\(=\dfrac{2}{3}\)

Answer 3