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\(\frac{\frac{3}{7}-\frac{3}{11}+\frac{3}{13}}{\frac{5}{7}-\frac{5}{11}+\frac{5}{13}}+\frac{\frac{1}{2}-\frac{1}{3}+\frac{1}{4}}{\frac{5}{4}-\frac{5}{6}+\frac{5}{8}}\)
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PL
13 tháng 12 2017
ta có \(\frac{\frac{3}{7}-\frac{3}{11}+\frac{3}{13}}{\frac{5}{7}-\frac{5}{11}+\frac{5}{13}}=\frac{3\left(\frac{1}{7}-\frac{1}{11}+\frac{1}{13}\right)}{5\left(\frac{1}{7}-\frac{1}{11}+\frac{1}{13}\right)}=\frac{3}{5}\)
và \(\frac{\frac{1}{2}-\frac{1}{3}+\frac{1}{4}}{\frac{5}{4}+\frac{5}{8}-\frac{5}{6}}=\frac{2\left(\frac{1}{2.2}-\frac{1}{3.2}+\frac{1}{4.2}\right)}{5\left(\frac{1}{4}+\frac{1}{8}-\frac{1}{6}\right)}=\frac{2\left(\frac{1}{4}+\frac{1}{8}-\frac{1}{6}\right)}{5\left(\frac{1}{4}+\frac{1}{8}-\frac{1}{6}\right)}=\frac{2}{5}\)
Vậy \(\frac{\frac{3}{7}-\frac{3}{11}+\frac{3}{13}}{\frac{5}{7}-\frac{5}{11}+\frac{5}{13}}+\frac{\frac{1}{2}-\frac{1}{3}+\frac{1}{4}}{\frac{5}{4}+\frac{5}{8}-\frac{5}{6}}=\frac{3}{5}+\frac{2}{5}=\frac{5}{5}=1\)
ĐS: 1
9 tháng 2 2017
\(\frac{\frac{3}{4}-\frac{3}{11}+\frac{3}{13}}{\frac{5}{7}-\frac{5}{11}+\frac{5}{13}}+\frac{\frac{1}{2}-\frac{1}{3}+\frac{1}{4}}{\frac{5}{4}-\frac{5}{6}+\frac{5}{8}}\)
\(=\frac{\frac{21}{44}+\frac{3}{13}}{\frac{20}{77}+\frac{5}{13}}+\frac{\frac{1}{6}+\frac{1}{4}}{\frac{5}{12}+\frac{5}{8}}\)
\(=\frac{\frac{405}{572}}{\frac{645}{1001}}+\frac{\frac{5}{12}}{\frac{25}{24}}\)
\(=\frac{1289}{860}\)
6 tháng 2 2017
\(\frac{\frac{3}{7}-\frac{3}{11}+\frac{3}{13}}{\frac{5}{7}-\frac{5}{11}+\frac{5}{13}}+\frac{\frac{1}{2}-\frac{1}{3}+\frac{1}{4}}{\frac{5}{4}-\frac{5}{6}+\frac{5}{8}}\)
\(=\frac{3\times\frac{1}{7}-3\times\frac{1}{11}+3\times\frac{1}{13}}{5\times\frac{1}{7}-5\times\frac{1}{11}+5\times\frac{1}{13}}+\frac{\frac{1}{2}-\frac{1}{3}+\frac{1}{4}}{\frac{5}{2}\times\frac{1}{2}-\frac{5}{2}\times\frac{1}{3}+\frac{5}{2}\times\frac{1}{4}}\)
\(=\frac{3\times\left(\frac{1}{7}-\frac{1}{11}+\frac{1}{13}\right)}{5\times\left(\frac{1}{7}-\frac{1}{11}+\frac{1}{13}\right)}+\frac{\frac{1}{2}-\frac{1}{3}+\frac{1}{4}}{\frac{5}{2}\times\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{4}\right)}\)
\(=\frac{3}{5}+\frac{1}{\frac{5}{2}}\)
\(=\frac{3}{5}+1\div\frac{5}{2}\)
\(=\frac{3}{5}+1\times\frac{2}{5}\)
\(=\frac{3}{5}+\frac{2}{5}\)
\(=\frac{5}{5}\)
\(=1\)
12 tháng 9 2015
có: chia 2 vế:
Vế 1 :
\(\frac{\frac{3}{7}-\frac{3}{11}+\frac{3}{13}}{\frac{5}{7}-\frac{5}{11}+\frac{5}{13}}=\frac{3\left(\frac{1}{7}-\frac{1}{11}+\frac{1}{13}\right)}{5\left(\frac{1}{7}-\frac{1}{11}+\frac{1}{13}\right)}=\frac{3}{5}\)
Vế 2 :
\(\frac{\frac{1}{2}-\frac{1}{3}+\frac{1}{4}}{\frac{5}{4}-\frac{5}{6}+\frac{5}{8}}=\frac{1.\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{4}\right)}{5\left(\frac{1}{4}-\frac{1}{6}+\frac{1}{8}\right)}=\frac{1\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{4}\right)}{5.2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{4}\right)}=\frac{1}{10}\)
=> 3/5 + 1/10 = 6/10 + 1/10 = 7/10
28 tháng 3 2018
=\(\frac{3\left(\frac{1}{1}-\frac{1}{11}+\frac{1}{13}\right)}{5\left(\frac{1}{7}-\frac{1}{11}+\frac{1}{13}\right)}+\frac{\frac{2}{4}+\frac{2}{6}+\frac{2}{8}}{5\left(\frac{1}{4}+\frac{1}{6}+\frac{1}{8}\right)}\)
=\(\frac{3}{5}+\frac{2\left(\frac{1}{4}+\frac{1}{6}+\frac{1}{8}\right)}{5\left(\frac{1}{4}+\frac{1}{6}+\frac{1}{8}\right)}\)=\(\frac{3}{5}+\frac{2}{5}=\frac{5}{5}=1\)
\(\frac{\frac{3}{7}-\frac{3}{11}+\frac{3}{13}}{\frac{5}{7}-\frac{5}{11}+\frac{5}{13}}+\frac{\frac{1}{2}-\frac{1}{3}+\frac{1}{4}}{\frac{5}{4}-\frac{5}{6}+\frac{5}{8}}\)
\(=\frac{3\left(\frac{1}{7}-\frac{1}{11}+\frac{1}{13}\right)}{5\left(\frac{1}{7}-\frac{1}{11}+\frac{1}{13}\right)}+\frac{4\left(\frac{1}{4}-\frac{1}{6}+\frac{1}{8}\right)}{5\left(\frac{1}{4}-\frac{1}{6}+\frac{1}{8}\right)}\)
\(=\frac{3}{5}+\frac{4}{5}=\frac{7}{5}\)
Ta có: \(\frac{\frac{3}{7}-\frac{3}{11}+\frac{3}{13}}{\frac{5}{7}-\frac{5}{11}+\frac{5}{13}}+\frac{\frac{1}{2}-\frac{1}{3}+\frac{1}{4}}{\frac{5}{4}-\frac{5}{6}+\frac{5}{8}}\)
\(=\frac{3\left(\frac{1}{7}-\frac{1}{11}+\frac{1}{13}\right)}{5\left(\frac{1}{7}-\frac{1}{11}+\frac{1}{13}\right)}+\frac{4\left(\frac{1}{4}-\frac{1}{6}+\frac{1}{8}\right)}{5\left(\frac{1}{4}-\frac{1}{6}+\frac{1}{8}\right)}\)
\(=\frac{3}{5}+\frac{4}{5}\)
\(=\frac{7}{5}\)