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a) \(\frac{34}{13}=2\frac{8}{13}\)
Vì 2 > 1 nên \(2\frac{8}{13}>1\frac{7}{9}\)
hay \(\frac{34}{13}>1\frac{7}{9}\)
b) \(\frac{7}{9}=1-\frac{2}{9}\)
\(\frac{13}{15}=1-\frac{2}{15}\)
Vì \(\frac{2}{9}>\frac{2}{15}\) nên \(\frac{7}{9}< \frac{13}{15}\)
a) Ta có:
\(1\frac{7}{9}=\frac{16}{9}=\frac{208}{117}\)
\(\frac{34}{13}=\frac{306}{117}\)
Vì \(306>208\)
\(\Rightarrow\frac{306}{117}>\frac{208}{117}\)
\(\Rightarrow\frac{34}{13}>1\frac{7}{9}\)
b) Ta có:
\(\frac{7}{9}=\frac{35}{45}\)
\(\frac{13}{15}=\frac{39}{45}\)
Vì \(39>35\)
\(\Rightarrow\frac{39}{45}>\frac{35}{45}\)
\(\Rightarrow\frac{13}{15}>\frac{7}{9}\)
\(\frac{x+2}{17}+\frac{x+4}{15}+\frac{x+6}{13}=\frac{x+8}{11}+\frac{x+10}{9}+\frac{x+12}{7}\)
\(\Rightarrow\left(\frac{x+2}{17}+1\right)+\left(\frac{x+4}{15}+1\right)+\left(\frac{x+6}{13}+1\right)-\left(\frac{x+8}{11}+1\right)-\left(\frac{x+10}{9}+1\right)-\left(\frac{x+12}{7}+1\right)=0\)
\(\Rightarrow\frac{x+19}{17}+\frac{x+19}{15}+\frac{x+19}{13}-\frac{x+19}{11}-\frac{x+19}{10}-\frac{x+19}{7}=0\)
\(\Rightarrow\left(x+19\right)(\frac{1}{17}+\frac{1}{15}+\frac{1}{13}-\frac{1}{11}-\frac{1}{9}-\frac{1}{7})\)
\(\Rightarrow x+19=0\)\(\left(Vì\frac{1}{17}+\frac{1}{15}+\frac{1}{13}-\frac{1}{11}-\frac{1}{9}-\frac{1}{7}\ne0\right)\)
\(\Rightarrow x=-19\)
Ta có : \(\frac{x+2}{17}+\frac{x+4}{15}+\frac{x+6}{13}=\frac{x+8}{11}+\frac{x+10}{9}+\frac{x+12}{7}\)
\(\Rightarrow\left(\frac{x+2}{17}+1\right)+\left(\frac{x+4}{15}+1\right)+\left(\frac{x+6}{13}+1\right)=\left(\frac{x+8}{11}+1\right)+\left(\frac{x+10}{9}+1\right)+\left(\frac{x+12}{7}+1\right)\)
\(\Rightarrow\frac{x+19}{17}+\frac{x+19}{15}+\frac{x+19}{13}-\frac{x+19}{11}-\frac{x+19}{9}-\frac{x+19}{7}=0\)
\(\Rightarrow\left(x+19\right)\left(\frac{1}{17}+\frac{1}{15}+\frac{1}{13}-\frac{1}{11}-\frac{1}{9}-\frac{1}{7}\right)=0\)
\(\Rightarrow x+19=0\Rightarrow x=-19\)
Đặt \(A=\frac{9}{1.2}+\frac{9}{2.3}+...+\frac{9}{99.100}\)
\(A=9.\left(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{99.100}\right)\)
\(A=9.\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}\right)\)
\(A=9.\left(1-\frac{1}{100}\right)\)
\(A=9.\frac{99}{100}=\frac{891}{100}\)
Ủng hộ mk nha !!! ^_^
\(\frac{9}{1.2}+\frac{9}{2.3}+\frac{9}{3.4}+.......+\frac{9}{99.100}\)
\(=9.\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+....+\frac{1}{99.100}\right)\)
\(=9.\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+....+\frac{1}{99}-\frac{1}{100}\right)\)
\(=9.\left(1-\frac{1}{100}\right)\)
\(=9.\frac{99}{100}=\frac{891}{100}\)
\(\Leftrightarrow\frac{34}{9}.x:\left(9+\frac{13}{9}\right)=34+\frac{1}{4}\)
\(\Leftrightarrow\frac{34}{9}.x:\frac{94}{9}=\frac{137}{4}\)
\(\Leftrightarrow\frac{17}{57}.x=\frac{137}{4}\Rightarrow x=\frac{17.4}{57.137}\)(tu tinh )