Câu 1:

$\begin{array}{l}a) x+\dfrac{4}{9.13}+\dfrac{4}{13.17}+\dfrac{4}{17.21}+...+\dfrac{4}{41.45}=10\\\Leftrightarrow x+\dfrac{1}{9}-\dfrac{1}{13}+\dfrac{1}{13}-\dfrac{1}{17}+\dfrac{1}{17}-\dfrac{1}{21}+\dfrac{1}{21}+...+\dfrac{1}{41}-\dfrac{1}{45}=10\\\Leftrightarrow x+\dfrac{1}{9}-\dfrac{1}{45}=10\\\Leftrightarrow x+\dfrac{4}{45}=10\\\Leftrightarrow x=10-\dfrac{4}{45}=\dfrac{446}{45} \end{array}$

$\begin{array}{l}b)\dfrac{2}{3}x-70\dfrac{10}{11}:\left ( \dfrac{131313}{151515}+\dfrac{131313}{353535}+\dfrac{131313}{636363}+\dfrac{131313}{999999} \right )=-5\\\Leftrightarrow \dfrac{2}{3}x-\dfrac{780}{11}:\left ( \dfrac{13}{15}+\dfrac{13}{35}+\dfrac{13}{63}+\dfrac{13}{99} \right )=-5\\\Leftrightarrow \dfrac{2}{3}x-\dfrac{780}{11}:\dfrac{52}{33}=-5\\\Leftrightarrow \dfrac{2}{3}x-45=-5\\\Leftrightarrow \dfrac{2}{3}x=40\\\Leftrightarrow x=60\end{array}$

Giải thích các bước giải:

 a) `x+ 4/(9.13) + 4/(13.17) + 4/(17.21) + ...... + 4/(41.45) = 10`

`=>x+ (4/(9.13) + 4/(13.17) + 4/(17.21) + ...... + 4/(41.45) )= 10`

`=>x+ (1/9-1/13 + 1/13-1/17 + 1/17-1/21 + ...... + 1/41-1/45 )= 10`

`=>x+ (1/9-1/45 )= 10`

`=>x+ 4/45= 10`

`=>x=9 41/45`

 b) `2/3x - 70 10/11 : ( 131313/151515 + 131313/353535 + 131313/636363 + 131313/999999 ) = -5`

`=>2/3x - 70 10/11 : ( 13/15 + 13/35 + 13/63 + 13/99 ) = -5`

Đến đó bạn làm tiếp đc mà !