3) \(58\left(3\dfrac{1}{29}-2\dfrac{1}{58}\right):\dfrac{1}{3}\)

\(=58\left(\dfrac{88}{29}-\dfrac{117}{58}\right)\cdot3\\ =\left(58\cdot\dfrac{88}{29}-58\cdot\dfrac{117}{58}\right)\cdot3\)

\(=\left(176-117\right)\cdot3\\ =59\cdot3\\ =177\)

4) \(A=1\dfrac{1}{2}\cdot1\dfrac{1}{3}\cdot1\dfrac{1}{4}\cdot1\dfrac{1}{5}\)

\(=\dfrac{3}{2}\cdot\dfrac{4}{3}\cdot\dfrac{5}{4}\cdot\dfrac{6}{5}\\ =\dfrac{3\cdot4\cdot5\cdot6}{2\cdot3\cdot4\cdot5}\\ =\dfrac{6}{2}\\ =3\)

a: =>15/5*34/17<x<120/15

=>6<x<8

=>x=7

b; =>20/5*58/29<x<112/11

=>8<x<112/11

=>x=9 hoặc x=10

ai có thể chỉ giúp tôi được ko vì tôi cần rất gấp

\(a,\dfrac{-5}{13}+\dfrac{8}{13}=\dfrac{3}{13}\\ b,\dfrac{5}{31}+\dfrac{-22}{31}=\dfrac{-17}{31}\\ c,\dfrac{-13}{43}+\dfrac{-40}{43}=\dfrac{-53}{43}\\ d,\dfrac{-3}{29}-\dfrac{16}{58}=\dfrac{-11}{29}\\ e,\dfrac{8}{40}-\dfrac{-36}{45}=1\\ f,\dfrac{-8}{18}-\dfrac{-15}{27}=\dfrac{1}{9}\\ g,\left(-2\right)+\dfrac{-5}{8}=\dfrac{-21}{8}\)

Ta có: \(\dfrac{x-1}{59}+\dfrac{x-2}{58}+\dfrac{x-3}{57}=\dfrac{x-4}{56}+\dfrac{x-5}{55}+\dfrac{x-6}{54}\)

\(\Leftrightarrow\dfrac{x-60}{59}+\dfrac{x-60}{58}+\dfrac{x-60}{57}-\dfrac{x-60}{56}-\dfrac{x-60}{55}-\dfrac{x-60}{54}=0\)

\(\Leftrightarrow x-60=0\)

hay x=60

Lại đăng nữa hả chíp chíp

\(D=\dfrac{1}{2}-\dfrac{1}{2^4}+\dfrac{1}{2^7}-\dfrac{1}{2^{10}}+....+\dfrac{1}{2^{55}}-\dfrac{1}{2^{58}}\\ \Rightarrow2^3D=\dfrac{1}{2^4}-\dfrac{1}{2^7}+\dfrac{1}{2^{10}}-\dfrac{1}{2^{13}}+...+\dfrac{1}{2^{58}}-\dfrac{1}{2^{61}}\\ \Rightarrow8D+D=\dfrac{1}{2}-\dfrac{1}{2^{61}}\\ \Rightarrow9D=\dfrac{1}{2}-\dfrac{1}{2^{61}}\\ \Rightarrow D=\dfrac{\dfrac{1}{2}-\dfrac{1}{2^{61}}}{9}\)

chữ đẹp hem:

\(\dfrac{x-1}{59}+\dfrac{x-2}{58}+\dfrac{x-3}{57}=\dfrac{x-4}{56}+\dfrac{x-5}{55}+\dfrac{x-6}{54}\)

\(\Leftrightarrow\dfrac{x-1}{59}-1+\dfrac{x-2}{58}-1+\dfrac{x-3}{57}=\dfrac{x-4}{56}-1+\dfrac{x-5}{55}-1+\dfrac{x-6}{54}-1\)

\(\Leftrightarrow\dfrac{x-60}{59}+\dfrac{x-60}{58}+\dfrac{x-60}{57}=\dfrac{x-60}{56}+\dfrac{x-60}{55}+\dfrac{x-60}{54}\)

\(\Leftrightarrow\left(x-60\right)\left(\dfrac{1}{59}+\dfrac{1}{58}+\dfrac{1}{57}-\dfrac{1}{56}-\dfrac{1}{55}-\dfrac{1}{54}\right)=0\)

\(\Leftrightarrow x-60=0\)

\(\Rightarrow x=60\)

vậy \(S=\left\{60\right\}\)

Sửa đề: \(A=\dfrac{1}{2}+\dfrac{1}{2^4}+\dfrac{1}{2^7}+....+\dfrac{1}{2^{58}}\)

Ta có : \(A=\dfrac{1}{2}+\dfrac{1}{2^4}+\dfrac{1}{2^7}+.....+\dfrac{1}{2^{58}}\)

\(\Rightarrow2^3A=2^3.\left(\dfrac{1}{2}+\dfrac{1}{2^4}+\dfrac{1}{2^7}+\dfrac{1}{2^{58}}\right)\)

\(\Rightarrow2^3A=1+\dfrac{1}{2}+\dfrac{1}{2^4}+.....+\dfrac{1}{2^{55}}\)

\(\Rightarrow2^3A-A=\left(1+\dfrac{1}{2}+\dfrac{1}{2^4}+\dfrac{1}{2^7}+...+\dfrac{1}{2^{55}}\right)-\left(\dfrac{1}{2}+\dfrac{1}{2^2}+\dfrac{1}{2^7}+....+\dfrac{1}{2^{58}}\right)\)\(\Rightarrow7A=1-\dfrac{1}{2^{58}}\Rightarrow A=\dfrac{1-\dfrac{1}{2^{58}}}{7}\)

Vậy...........

~ Học tốt nha ~

\(A=\dfrac{1}{2}+\dfrac{1}{2^4}+\dfrac{1}{2^7}+...+\dfrac{1}{2^{58}}\\ 2^3\cdot A=\dfrac{2^3}{2}+\dfrac{2^3}{2^4}+\dfrac{2^3}{2^7}+...+\dfrac{2^3}{2^{58}}\\ 8A=4+\dfrac{1}{2}+\dfrac{1}{2^4}+...+\dfrac{1}{2^{55}}\\ 8A-A=\left(4+\dfrac{1}{2}+\dfrac{1}{2^4}+...+\dfrac{1}{2^{55}}\right)-\left(\dfrac{1}{2}+\dfrac{1}{2^4}+\dfrac{1}{2^7}+...+\dfrac{1}{2^{58}}\right)\\ 7A=4-\dfrac{1}{2^{58}}\\ A=\dfrac{4-\dfrac{1}{2^{58}}}{7}\)

\(\dfrac{x+1}{58}+\dfrac{x+2}{57}=\dfrac{x+3}{56}+\dfrac{x+4}{55}\)

\(\Leftrightarrow\left(\dfrac{x+1}{58}+1\right)+\left(\dfrac{x+2}{57}+1\right)=\left(\dfrac{x+3}{56}+1\right)+\left(\dfrac{x+4}{55}+1\right)\)

\(\Leftrightarrow\dfrac{x+59}{58}+\dfrac{x+59}{57}-\dfrac{x+59}{56}-\dfrac{x+59}{55}=0\)

\(\Leftrightarrow\left(x+59\right)\left(\dfrac{1}{58}+\dfrac{1}{57}-\dfrac{1}{56}-\dfrac{1}{55}\right)=0\)

\(\Leftrightarrow x+59=0\)

\(\Leftrightarrow x=-59\)

\(\dfrac{x+1}{58}+\dfrac{x+2}{59}=\dfrac{x+3}{56}+\dfrac{x+4}{55}\)

\(\Leftrightarrow\dfrac{x+1}{58}+1+\dfrac{x+2}{57}+1=\dfrac{x+3}{56}+1+\dfrac{x+4}{55}+1\)

\(\Leftrightarrow\dfrac{x+59}{58}+\dfrac{x+59}{57}=\dfrac{x+59}{56}+\dfrac{x+59}{55}\)

\(\Leftrightarrow\dfrac{x+59}{58}+\dfrac{x+59}{57}-\dfrac{x+59}{56}-\dfrac{x+59}{55}=0\)

\(\Leftrightarrow\left(x+59\right)\left(\dfrac{1}{58}+\dfrac{1}{57}-\dfrac{1}{56}-\dfrac{1}{55}\right)=0\)

Mà \(\dfrac{1}{58}+\dfrac{1}{57}-\dfrac{1}{56}-\dfrac{1}{55}\ne0\)

\(\Rightarrow x+59=0\)

\(\Leftrightarrow x=-59\)

Vậy: \(S=\left\{-59\right\}\)

Giải

\(\dfrac{x+1}{58}+\dfrac{x+2}{59}=\dfrac{x+3}{56}+\dfrac{x+4}{55}\)

⇔\(\left(\dfrac{x+1}{58}+1\right)+\left(\dfrac{x+2}{57}+1\right)=\left(\dfrac{x+3}{56}+1\right)+\left(\dfrac{x+4}{55}+1\right)\)

⇔\(\dfrac{x+59}{58}+\dfrac{x+59}{57}-\dfrac{x+59}{56}-\dfrac{x+59}{55}=0\)

⇔\(\left(x+59\right)\left(\dfrac{1}{58}+\dfrac{1}{57}-\dfrac{1}{56}-\dfrac{1}{55}\right)=0\)

⇔\(x+59=0\)

⇔\(x=-59\)

\(=4+\dfrac{5}{58}-3-\dfrac{1}{2}+8+\dfrac{15}{29}-3-\dfrac{5}{58}+7+\dfrac{14}{29}=13+\dfrac{1}{2}=\dfrac{27}{2}\)