1) 1/3 x 1/2 x 3/7 = 3/42 = 1/14

2) 5/4 x 1/3 +1/7 = 5/12 + 1/7 = 35/84 + 12/84 = 47/84

3) 8 x ( 8/9 - 2/3 ) = 8 x 2/9 = 16/9

4) 5/6 x 48/20 x 1/2 = 240/240 = 1

5) ( 2/5 + 3/4 ) + 8 = 23/20 + 8 = 23//20 + 160/20 = 183/20

6) 10 x ( 1/2 - 1/5 ) = 10 x 3/10 = 10/1 x 3/10 = 30/10 = 3

1: \(=\dfrac{1}{3}\cdot\dfrac{3}{7}\cdot\dfrac{1}{2}=\dfrac{1}{7\cdot2}=\dfrac{1}{14}\)

2: =5/12+1/7

=35/84+12/84=47/84

3: =8(8/9-6/9)

=8*2/9=16/9

4: \(=\dfrac{5}{12}\cdot\dfrac{12}{5}=1\)

5: =16/5+6

=16/5+30/5=46/5

6: =10*1/2-10*1/5

=5-2=3

a)\(\frac{5}{6}+\frac{3}{4}x=3\Leftrightarrow\frac{3}{4}x=\frac{13}{6}\Leftrightarrow x=\frac{26}{9}\)

b)\(\frac{8}{x}\cdot\frac{3}{4}=\frac{9}{10}\Leftrightarrow\frac{8}{x}=\frac{6}{5}\Leftrightarrow x=\frac{8\cdot5}{6}=\frac{20}{3}\)

c)\(3\cdot\left(x+\frac{1}{2}\right)-\frac{1}{3}=\frac{2}{5}\Leftrightarrow3\left(x+\frac{1}{2}\right)=\frac{11}{15}\Leftrightarrow x+\frac{1}{2}=\frac{11}{45}\Leftrightarrow x=-\frac{23}{90}\)

d)\(\frac{1}{4}+\frac{x}{3}=\frac{5}{6}\Leftrightarrow\frac{x}{3}=\frac{7}{12}\Leftrightarrow x=\frac{7\cdot3}{12}=\frac{7}{4}\)

Bạn ơi , cái dấu hai chiều là sao ? trả lời nhanh cho mình nhé !

là dấu tương đương đó bạn

\(\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+...+\dfrac{1}{x.\left(x+1\right)}=1\)

\(\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+...+\dfrac{1}{x.\left(x+1\right)}=1\)

\(\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{x}-\dfrac{1}{x+1}=1\)

MK chưa làm xong đợi mk ăn cơm xong làm nha

nhân cả 2 vế của đẳng thức với 1/2 ta được

\(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+.....+\frac{1}{x\left(x+1\right)}=\frac{2014}{2015}\)

\(=\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+.....+\frac{1}{x\left(x+1\right)}=\frac{2014}{2015}\)

\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-......+\frac{1}{x}-\frac{1}{x+1}=\frac{2014}{2015}\)

\(=\frac{1}{2}-\frac{1}{x+1}=\frac{2014}{2015}\)

\(=>\frac{1}{x+1}=\frac{1}{2}-\frac{2014}{2015}\)

        \(\frac{1}{x+1}=-\frac{2013}{4030}\)

hay \(1:\left(x+1\right)=-\frac{2013}{4030}\)

       \(x+1=-\frac{4030}{2013}\)

\(=>x=-\frac{6043}{2013}\)

\(\dfrac{1}{3}+\dfrac{1}{6}+\dfrac{1}{10}+...+\dfrac{2}{x\left(x+1\right)}=\dfrac{4020}{2011}\)

\(\Rightarrow\dfrac{2}{6}+\dfrac{2}{12}+\dfrac{2}{20}+...+\dfrac{2}{x\left(x+1\right)}=\dfrac{4020}{2011}\)

\(\Rightarrow\dfrac{2}{2.3}+\dfrac{2}{3.4}+\dfrac{2}{4.5}+...+\dfrac{2}{x\left(x+1\right)}=\dfrac{4020}{2011}\)

\(\Rightarrow2\left(\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+...+\dfrac{1}{x\left(x+1\right)}\right)=\dfrac{4020}{2011}\)

\(\Rightarrow\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+...+\dfrac{1}{x\left(x+1\right)}=\dfrac{4020}{2011}:2\)

\(\Rightarrow\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+...+\dfrac{1}{x}-\dfrac{1}{x+1}=\dfrac{2010}{2011}\)

\(\Rightarrow\dfrac{1}{2}-\dfrac{1}{x+1}=\dfrac{2010}{2011}\)

\(\Rightarrow\dfrac{1}{x+1}=\dfrac{1}{2}-\dfrac{2010}{2011}\)

\(\Rightarrow\dfrac{1}{x+1}=-\dfrac{2009}{4022}\)

\(\Rightarrow4022=-2009\left(x+1\right)\)

\(\Rightarrow4022=-2009x-2009\)

\(\Rightarrow2009x=-2009-4022\)

\(\Rightarrow2009x=-6031\)

\(\Rightarrow x=-\dfrac{6031}{2009}\)