`(-12)/(9-x) =4/5`

`=> -12.5=(9-x).4`

`=> -60=(9-x).4`

`=> (9-x).4=-60`

`=>9-x=-60:4`

`=>9-x=-15`

`=>x=9-(-15)`

`=>x=9+15`

`=>x= 24`

\(=5\left(\dfrac{1}{12}+\dfrac{1}{20}+\dfrac{1}{30}+\dfrac{1}{42}+\dfrac{1}{56}\right)\)

\(=5\left(\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+...+\dfrac{1}{7}-\dfrac{1}{8}\right)\)

\(=5\cdot\dfrac{5}{24}=\dfrac{25}{24}\)

`5/12 + 5/20 + 5/30 + 5/42 + 5/56`

`= 5/(3.4) + 5/(4.5) + 5/(5.6) + 5/(6.7) + 5/(7.8)`

`= 5 . (1/(3.4) + 1/(4.5) + ... + 5/(7.8))`

`= 5 . (1/3 - 1/4 + 1/4 - 1/5 + ...+ 1/7 - 1/8)`

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

`= 5 . 5/24 = 25/24`

Lời giải:

Vì $a,b$ là số tự nhiên nên $2a+1,b-2$ là số nguyên

$(2a+1)(b-2)=12$ nên $2a+1$ là ước của $12$
Mà $2a+1$ là số tự nhiên lẻ nên $2a+1\in\left\{1;3\right\}$

Nếu $2a+1=1$ thì $b-2=12:1=12$

$\Rightarrow a=0; b=14$ (thỏa mãn)

Nếu $2a+1=3$ thì $b-2=12:3=4$

$\Rightarrow a=1; b=6$ (thỏa mãn)

\(-\dfrac{5}{7}\times\dfrac{2}{13}+\dfrac{-5}{7}\times\dfrac{3}{13}-\dfrac{5}{7}\times\dfrac{8}{13}\)

\(=-\dfrac{5}{7}\left(\dfrac{2}{13}+\dfrac{3}{13}+\dfrac{8}{13}\right)\)

\(=-\dfrac{5}{7}\times\dfrac{13}{13}\)

\(=-\dfrac{5}{7}\times1=-\dfrac{5}{7}\)

\(-\dfrac{5}{7}.\dfrac{2}{13}+\dfrac{-5}{7}.\dfrac{3}{13}-\dfrac{5}{7}.\dfrac{8}{13}\)

\(=-\dfrac{10}{91}-\dfrac{15}{91}-\dfrac{40}{91}\)

\(=\dfrac{-10-15-40}{91}\)

\(=-\dfrac{65}{91}=-\dfrac{5}{7}\)

\(\dfrac{-5}{7}.\dfrac{2}{13}+\left(\dfrac{-5}{7}\right).\dfrac{3}{13}-\dfrac{5}{7}.\dfrac{8}{13}\)

\(=\dfrac{5}{7}.\left(\dfrac{-2}{13}+\dfrac{-3}{13}-\dfrac{8}{13}\right)\)

\(=\dfrac{5}{7}.\left(-1\right)\)

\(=-\dfrac{5}{7}\)

\(#PaooNqoccc\)

`6/7 . 8/13 +6/7 . 9/13+3/13 . 6/7`

`=6/7 . (8/13+9/13+3/13)`

`=6/7 . 20/13`

`=120/91`

\(\dfrac{6}{7}.\dfrac{8}{13}+\dfrac{6}{7}.\dfrac{9}{13}+\dfrac{3}{13}.\dfrac{6}{7}\)

\(=\dfrac{6}{7}.\left(\dfrac{8}{13}+\dfrac{9}{13}+\dfrac{3}{13}\right)\)

\(=\dfrac{6}{7}.\left(\dfrac{8+9+3}{13}\right)\)

\(=\dfrac{6}{7}.\dfrac{20}{13}\)

\(=\dfrac{6.20}{7.13}\)

\(=\dfrac{120}{91}\)

`6/7 . 8/13 + 6/7 . 9/13 + 3/13 . 6/7`

`= 6/7 . ( 8/13 + 9/13 + 3/13)`

`=6/7 . 20/13`

`= 120/91`

\(=\dfrac{1}{3}:\dfrac{7\cdot\left(5+3\right)}{18\cdot\left(53-11\right)}\) 

\(=\dfrac{1}{3}:\dfrac{7\cdot8}{18\cdot42}\) 

\(=\dfrac{1}{3}:\dfrac{7\cdot2\cdot2\cdot2}{3\cdot3\cdot2\cdot2\cdot3\cdot7}\)

\(=\dfrac{1}{3}:\dfrac{2}{3\cdot3\cdot3}\)

\(=\dfrac{1}{3}\cdot\dfrac{27}{2}\)

\(=\dfrac{9}{2}\)

\(-\dfrac{3}{7}\times\dfrac{15}{13}-\dfrac{3}{7}\times\dfrac{11}{13}-\dfrac{3}{7}\)

\(=-\dfrac{3}{7}\left(\dfrac{15}{13}+\dfrac{11}{13}+1\right)\)

\(=-\dfrac{3}{7}\left(\dfrac{15}{13}+\dfrac{11}{13}+\dfrac{13}{13}\right)\)

\(=-\dfrac{3}{7}\times\dfrac{39}{13}=-\dfrac{3}{7}\times3=-\dfrac{9}{7}\)

1<4/x<=-5/8

mà 1>-5/8

nên \(x\in\varnothing\)

`S_1 = 5/(1.4) + 5/(4.7) +...+ 5/(97.100)`

`S_1 = 5 (1/(1.4) + 1/(4.7) +...+ 1/(97.100))`

`S_1 = 5/3 (3/(1.4) + 3/(4.7) +...+ 3/(97.100))`

`S_1 = 5/3 (1 - 1/4 + 1/4 - 1/7 + ...+ 1/97 - 1/100)`

`S_1 = 5/3 (1 - 1/100)`

`S_1 = 5/3 . 99/100`

`S_1 = 33/20`