Bài 2:
a) \(\dfrac{17}{6}-\left(x-\dfrac{7}{6}\right)=\dfrac{7}{4}\)
\(\Rightarrow\dfrac{17}{6}-x+\dfrac{7}{6}=\dfrac{7}{4}\)
\(\Rightarrow4-x=\dfrac{7}{4}\)
\(\Rightarrow x=4-\dfrac{7}{4}\)
\(\Rightarrow x=\dfrac{9}{4}\)
b) \(\dfrac{4}{3}+\left(1,25-x\right)=2,25\)
\(\Rightarrow\dfrac{4}{3}+1,25-x=2,25\)
\(\Rightarrow\dfrac{4}{3}-x=2,25-1,25\)
\(\Rightarrow\dfrac{4}{3}-x=1\)
\(\Rightarrow x=\dfrac{4}{3}-1=\dfrac{1}{3}\)
c) \(2x-3=x+\dfrac{1}{2}\)
\(\Rightarrow2x-x=\dfrac{1}{2}+3\)
\(\Rightarrow x\cdot\left(2-1\right)=\dfrac{7}{2}\)
\(\Rightarrow x=\dfrac{7}{2}\)
d) \(4x-\left(2x+1\right)=3-\dfrac{1}{3}+x\)
\(\Rightarrow4x-2x-1=3-\dfrac{1}{3}+x\)
\(\Rightarrow x\cdot\left(4-2\right)-1=\dfrac{8}{3}+x\)
\(\Rightarrow2x-1=\dfrac{8}{3}+x\)
\(\Rightarrow2x-x=\dfrac{8}{3}+1\)
\(\Rightarrow x=\dfrac{11}{3}\)
Bài 3:
a) \(\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+\dfrac{1}{3\cdot4}+...+\dfrac{1}{1999\cdot2000}\)
\(=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{1999}-\dfrac{1}{2000}\)
\(=1-\dfrac{1}{2000}\)
\(=\dfrac{1999}{2000}\)
b) \(\dfrac{1}{1\cdot4}+\dfrac{1}{4\cdot7}+\dfrac{1}{7\cdot10}+...+\dfrac{1}{100\cdot103}\)
\(=\dfrac{1}{3}\cdot3\cdot\left(\dfrac{1}{1\cdot4}+\dfrac{1}{4\cdot7}+\dfrac{1}{7\cdot10}+...+\dfrac{1}{100\cdot103}\right)\)
\(=\dfrac{1}{3}\cdot\left(\dfrac{3}{1\cdot4}+\dfrac{3}{4\cdot7}+...+\dfrac{3}{100\cdot103}\right)\)
\(=\dfrac{1}{3}\cdot\left(1-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{10}+...+\dfrac{1}{100}-\dfrac{1}{103}\right)\)
\(=\dfrac{1}{3}\cdot\left(1-\dfrac{1}{103}\right)\)
\(=\dfrac{1}{3}\cdot\dfrac{102}{103}\)
\(=\dfrac{34}{103}\)
c) \(\dfrac{8}{9}-\dfrac{1}{72}-\dfrac{1}{56}-\dfrac{1}{42}-...-\dfrac{1}{6}-\dfrac{1}{2}\)
\(=\dfrac{8}{9}-\left(\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+\dfrac{1}{3\cdot4}+...+\dfrac{1}{8\cdot9}\right)\)
\(=\dfrac{8}{9}-\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{8}-\dfrac{1}{9}\right)\)
\(=\dfrac{8}{9}-\left(1-\dfrac{1}{9}\right)\)
\(=\dfrac{8}{9}-\dfrac{8}{9}\)
\(=0\)
2:
a: =>x-7/6=17/6-7/4=13/12
=>x=13/12+7/6=9/4
b: =>1,25-x=9/4-4/3=11/12
=>x=5/4-11/12=15/12-11/12=4/12=1/3
c: =>2x-x=3+1/2
=>x=7/2
d: =>4x-2x-1=x+8/3
=>2x-1=x+8/3
=>x=11/3