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\(\Leftrightarrow\frac{1}{2}\left(\frac{2}{1\cdot3}+\frac{2}{3\cdot5}+...+\frac{2}{\left(5x+1\right)\left(5x+3\right)}\right)=\frac{11}{23}\)
\(\Leftrightarrow\frac{1}{2}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{5x+1}-\frac{1}{5x+3}\right)=\frac{11}{23}\)
\(\Leftrightarrow1-\frac{1}{5x+3}=\frac{22}{23}\)
\(\Leftrightarrow\frac{1}{5x+3}=\frac{1}{23}\)
\(\Leftrightarrow5x+3=23\Leftrightarrow x=4\) ( TM )
\(\frac{1}{1.3}+\frac{1}{3.5}+...+\frac{1}{\left(5x+1\right).\left(5x+3\right)}=\frac{11}{23}\)
\(\Rightarrow\frac{1}{2}\left(\frac{2}{1.3}+\frac{2}{3.5}+...+\frac{2}{\left(5x+1\right)\left(5x+3\right)}\right)=\frac{11}{23}\)
\(\Rightarrow\frac{1}{2}\left(1-\frac{1}{3}+...+\frac{1}{\left(5x+1\right)}-\frac{1}{\left(5x+3\right)}\right)=\frac{11}{23}\)
\(\Rightarrow1-\frac{1}{\left(5x+3\right)}=\frac{11}{23}:\frac{1}{2}\)
\(\Rightarrow\frac{1}{5x+3}=\frac{1}{23}\)
\(\Rightarrow5x+3=23\)
\(\Rightarrow5x=23-3\)
\(\Rightarrow x=20:5\)
\(\Rightarrow x=4\)
1)\(1\frac{3}{4}-1\frac{3}{8}:\left(\frac{3}{8}+\frac{9}{20}\right)=\frac{7}{4}-\frac{11}{8}:\frac{33}{40}=\frac{7}{4}-\frac{5}{3}=\frac{1}{12}\)
Bài giải:
Câu 1: a, \(\left(-2\right).4.5.38.\left(-25\right)\)
\(=\left[\left(-2\right).5\right].\left[4.\left(-25\right)\right].38\)
\(=\left(-10\right).\left(-100\right).38\)
\(=1000.38=38000\)
b,\(\frac{1}{3}+\frac{3}{8}-\frac{7}{12}\)
\(=\left(\frac{1}{3}+\frac{3}{8}\right)-\frac{7}{12}\)
\(=\frac{17}{24}-\frac{7}{12}=\frac{1}{8}\)
c, \(\frac{-5}{8}.\frac{5}{12}+\frac{-5}{8}.\frac{7}{12}+2\frac{1}{8}\)
\(=\frac{-5}{8}.\left(\frac{5}{12}+\frac{7}{12}\right)+\frac{17}{8}\)
\(=\frac{-5}{8}.1+\frac{17}{8}\)
\(=\frac{3}{2}\)
Câu 2: a, \(x-\frac{2}{5}=0,24\)
\(x-0,4=0,24\)
\(x=0,24+0,4\)
\(\Rightarrow x=0,64\left(\frac{16}{25}\right)\)
b,\(\frac{2}{3}.x+\frac{1}{12}=\frac{1}{10}\)
\(\frac{2}{3}.x=\frac{1}{10}-\frac{1}{12}\)
\(\frac{2}{3}.x=\frac{1}{60}\)
\(x=\frac{1}{60}:\frac{2}{3}\)
\(\Rightarrow x=\frac{1}{40}\)
c, \(\left(3\frac{1}{2}-2x\right).1\frac{1}{3}=7\frac{1}{3}\)
\(\frac{7}{2}-2x=\frac{22}{3}:\frac{4}{3}\)
\(\frac{7}{2}-2x=\frac{11}{2}\)
\(2x=\frac{7}{2}-\frac{11}{2}\)
\(2x=-2\)
\(\Rightarrow x=-2:2\)
\(x=-1\)
Ta có A=1.2.3....9-1.2.3....8-1.2.3...8.8
suy ra A=8!.9-8!-8!.8
suy ra A=8!.(9-1-8)
suy ra A=8!.0
suy ra A=0