Câu 1: 

\(\Rightarrow \left[\begin{array}{} x+\frac{1}{2}=0\\ \frac{2}{3}-2x=0 \end{array} \right.\)

\(\Leftrightarrow \left[\begin{array}{} x=\frac{-1}{2}\\ x=\frac{1}{3} \end{array} \right.\)

Vậy phương trình có tập nghiệm S={\(\frac{-1}{2};\frac{1}{3}\)}

Câu 2: 

\(\Rightarrow \left[\begin{array}{} 3x-10=0\\ 5-\frac{1}{2}x=0 \end{array} \right.\)

\(\Leftrightarrow \left[\begin{array}{} x-=\frac{10}{3}\\ x=10 \end{array} \right.\)

Vậy phương trình có tập nghiệm S={\(10;\frac{10}{3}\)}

Câu 3: 

\(\Leftrightarrow \frac{1}{3}x=\frac{65}{4}-\frac{53}{4}\)

\( \Leftrightarrow \frac{1}{3}x=\frac{12}{4}\)

\(\Leftrightarrow x=9\)

Vậy phương trình có tập nghiệm S={9}

Câu 4: 

\(\Leftrightarrow \frac{2}{3}x=\frac{2}{3}\)

\(\Leftrightarrow x=1\)

Vậy phương trình có tập nghiệm S={1}

Câu 5: 

\(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{x(x+1)}=\frac{2010}{2011}\)

\(\Leftrightarrow 1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{x}-\frac{1}{x+1}=\frac{2010}{2011}\)

\(\Leftrightarrow 1-\frac{1}{x+1}=\frac{2010}{2011}\)

\(\Leftrightarrow \frac{x}{x+1}=\frac{2010}{2011}\)

\(\Rightarrow 2010x+2010=2011x\)

\(\Leftrightarrow x=2010\)

Vậy phương trình có tập nghiệm S={2010}

cảm ơn bạn Hoàng Bình Bảo nha nhưng mà đây là toán lớp 6 mà bạn 

Giải:

1)

a: \(A=\dfrac{-7}{28}\cdot\dfrac{15}{25}=\dfrac{-1}{4}\cdot\dfrac{3}{5}=\dfrac{-3}{20}\)

b: \(B=\dfrac{-5\cdot7}{14\cdot\left(-3\right)}=\dfrac{35}{42}=\dfrac{5}{6}\)

c: \(C=\dfrac{-1}{5}-\dfrac{1}{5}\cdot\dfrac{3}{5}=\dfrac{-1}{5}-\dfrac{3}{25}=\dfrac{-8}{25}\)

d: \(D=\dfrac{-3}{4}-\dfrac{1}{4}=-1\)

e: \(E=\dfrac{-4}{5}\left(1-\dfrac{15}{16}\right)=\dfrac{-4}{5}\cdot\dfrac{1}{16}=\dfrac{-1}{20}\)

f: \(F=\dfrac{6-7}{4}\cdot\dfrac{4+12}{22}=\dfrac{-1}{4}\cdot\dfrac{8}{11}=\dfrac{-2}{11}\)

p: \(F=\dfrac{1}{3}\left(\dfrac{3}{3\cdot6}+\dfrac{3}{6\cdot9}+\dfrac{3}{9\cdot12}+...+\dfrac{3}{30\cdot33}\right)\)

\(=\dfrac{1}{3}\left(\dfrac{1}{3}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{9}+...+\dfrac{1}{30}-\dfrac{1}{33}\right)\)

\(=\dfrac{1}{3}\cdot\dfrac{10}{33}=\dfrac{10}{99}\)

n: \(F=2\left(\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{6}+...+\dfrac{1}{2008}-\dfrac{1}{2010}\right)\)

\(=2\cdot\dfrac{502}{1005}=\dfrac{1004}{1005}\)

m: \(=\left(3-\dfrac{7}{3}+\dfrac{1}{4}\right):\left(4-\dfrac{31}{6}+\dfrac{9}{4}\right)\)

\(=\dfrac{36-28+3}{12}:\dfrac{48-62+27}{12}\)

\(=\dfrac{11}{13}\)

Ta có:B=1\(\dfrac{6}{41}\)( \(\dfrac{12+\dfrac{12}{19}-\dfrac{12}{37}-\dfrac{12}{53}}{3+\dfrac{1}{3}-\dfrac{3}{37}-\dfrac{3}{53}}:\dfrac{4+\dfrac{4}{17}+\dfrac{4}{19}+\dfrac{4}{2006}}{5+\dfrac{5}{17}+\dfrac{5}{19}+\dfrac{5}{2006}}\) )

B=\(\dfrac{47}{41}\) [\(\dfrac{12\left(1+\dfrac{1}{19}-\dfrac{1}{37}-\dfrac{1}{53}\right)}{3\left(1+\dfrac{1}{3}-\dfrac{1}{37}-\dfrac{1}{53}\right)}:\dfrac{4\left(\dfrac{1}{17}+\dfrac{1}{19}+\dfrac{1}{2006}\right)}{5\left(1+\dfrac{1}{17}+\dfrac{1}{19}+\dfrac{1}{2006}\right)}\) B = \(\dfrac{47}{41}\) [ \(\dfrac{12}{3}:\dfrac{4}{5}\)]

B = \(\dfrac{47}{41}\)[ 4 . \(\dfrac{5}{4}\)]

B = \(\dfrac{47}{41}.5\)

B = \(\dfrac{235}{41}\)

Chúc bn hc tốt!!!

\(A=\dfrac{636363\cdot37-373737\cdot63}{1+2+3+...+2006}\)

\(=\dfrac{37^2\cdot3^3\cdot7^2\cdot13-37^2\cdot3^3\cdot7^2\cdot13}{\left(2006+1\right)\cdot1003}\)

=0

\(\)\(\left|1-\dfrac{x}{5}-\dfrac{4}{3}\right|=\dfrac{53}{15}\)

=> 1-\(\dfrac{x}{5}\)-\(\dfrac{4}{3}\)=\(\dfrac{53}{15}\) hoặc 1-\(\dfrac{x}{5}\)-\(\dfrac{4}{3}\)=\(\dfrac{-53}{15}\)

* 1-\(\dfrac{x}{5}\)-\(\dfrac{4}{3}\)=\(\dfrac{53}{15}\) * 1-\(\dfrac{x}{5}\)-\(\dfrac{4}{3}\)=\(\dfrac{-53}{15}\)

1-\(\dfrac{4}{3}\)-\(\dfrac{x}{5}\)=\(\dfrac{53}{15}\) 1-\(\dfrac{4}{3}\)-\(\dfrac{x}{5}\)=\(\dfrac{-53}{15}\)

\(\dfrac{-1}{3}\)-\(\dfrac{x}{5}\)=\(\dfrac{53}{15}\) \(\dfrac{-1}{3}\)-\(\dfrac{x}{5}\)=\(\dfrac{-53}{15}\)

\(\dfrac{x}{5}\)=\(\dfrac{-1}{3}\)\(-\dfrac{53}{15}\) \(\dfrac{x}{5}\)=\(\dfrac{-1}{3}\)+\(\dfrac{53}{15}\)

\(\dfrac{x}{5}\)= \(\dfrac{-58}{15}\) \(\dfrac{x}{5}\)= \(\dfrac{16}{5}\)

=> x=-58.5:15 => x=16.5:5

x=\(\dfrac{-58}{3}\) x =16

Vậy x=​\(\dfrac{-58}{3}\) hoặc x=16

\(\left|1-\dfrac{x}{5}-\dfrac{4}{3}\right|=\dfrac{53}{15}\Leftrightarrow\left|\dfrac{-1}{3}-\dfrac{x}{5}\right|=\dfrac{53}{15}\)

th1: \(\dfrac{-1}{3}-\dfrac{x}{5}\ge0\Leftrightarrow-\dfrac{x}{5}\ge\dfrac{1}{3}\Leftrightarrow x\le\dfrac{1}{3}.-5=\dfrac{-5}{3}\)

\(\Rightarrow\left|\dfrac{-1}{3}-\dfrac{x}{5}\right|=\dfrac{53}{15}\Leftrightarrow\dfrac{-1}{3}-\dfrac{x}{5}=\dfrac{53}{15}\Leftrightarrow-\dfrac{x}{5}=\dfrac{53}{15}+\dfrac{1}{3}\)

\(\Leftrightarrow-\dfrac{x}{5}=\dfrac{58}{15}\Leftrightarrow x=\dfrac{58}{15}.-5=\dfrac{-58}{3}\left(tmđk\right)\)

th2: \(\dfrac{-1}{3}-\dfrac{x}{5}< 0\Leftrightarrow-\dfrac{x}{5}< \dfrac{1}{3}\Leftrightarrow x>\dfrac{1}{3}.-5=\dfrac{-5}{3}\)

\(\Rightarrow\left|\dfrac{-1}{3}-\dfrac{x}{5}\right|=\dfrac{53}{15}\Leftrightarrow-\left(\dfrac{-1}{3}-\dfrac{x}{5}\right)=\dfrac{53}{15}\Leftrightarrow\dfrac{1}{3}+\dfrac{x}{5}=\dfrac{53}{15}\)

\(\Leftrightarrow\dfrac{x}{5}=\dfrac{53}{15}-\dfrac{1}{3}\Leftrightarrow\dfrac{x}{5}=\dfrac{16}{5}\Leftrightarrow x=\dfrac{16}{5}.5=16\left(tmđk\right)\)

vậy \(x=\dfrac{-58}{3};x=16\)

\(-1\dfrac{1}{5}.\dfrac{12+\dfrac{4}{3}-\dfrac{12}{37}-\dfrac{12}{35}}{3+\dfrac{1}{3}-\dfrac{3}{37}-\dfrac{3}{35}}:\dfrac{4+\dfrac{4}{17}+\dfrac{4}{19}+\dfrac{4}{2003}}{5+\dfrac{5}{17}+\dfrac{5}{19}+\dfrac{5}{2003}}\)

\(=\dfrac{-6}{5}.\dfrac{4\left(3+\dfrac{1}{3}-\dfrac{3}{37}-\dfrac{3}{35}\right)}{3+\dfrac{1}{3}-\dfrac{3}{37}-\dfrac{3}{35}}:\dfrac{4\left(1+\dfrac{1}{17}+\dfrac{1}{19}+\dfrac{1}{2003}\right)}{5\left(1+\dfrac{1}{17}+\dfrac{1}{19}+\dfrac{1}{2003}\right)}\)

\(=\dfrac{-6}{5}.4:\dfrac{4}{5}\)

\(=\dfrac{-6.4.5}{5.4}=-6\)

= -4 đúng không

\(-1\dfrac{1}{5}.\dfrac{12+\dfrac{4}{3}-\dfrac{12}{37}-\dfrac{12}{35}}{3+\dfrac{1}{3}-\dfrac{3}{37}-\dfrac{3}{53}}:\dfrac{4+\dfrac{4}{17}+\dfrac{4}{19}+\dfrac{4}{2003}}{5+\dfrac{5}{17}+\dfrac{5}{19}+\dfrac{5}{2003}}\)

\(=\dfrac{-6}{5}.\dfrac{4\left(3+\dfrac{1}{3}-\dfrac{3}{37}-\dfrac{3}{53}\right)}{3+\dfrac{1}{3}-\dfrac{3}{37}-\dfrac{3}{53}}:\dfrac{4\left(1+\dfrac{1}{17}+\dfrac{1}{19}+\dfrac{1}{2003}\right)}{5\left(1+\dfrac{1}{17}+\dfrac{1}{19}+\dfrac{1}{2003}\right)}\)

\(=\dfrac{-6}{5}.\dfrac{4}{3}:\dfrac{4}{5}\)

\(=\dfrac{-6.4.5}{5.3.4}=\dfrac{-6}{3}=-2\)

Vậy...

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