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\(\frac{\frac{1}{9}-\frac{1}{7}-\frac{1}{11}}{\frac{1}{9}-\frac{1}{7}-\frac{1}{11}}+\frac{\frac{3}{5}-\frac{3}{25}-\frac{3}{125}-\frac{3}{625}}{\frac{4}{5}-\frac{4}{25}-\frac{4}{125}-\frac{4}{625}}\)
= \(1+\frac{3.\left(\frac{1}{5}-\frac{1}{25}-\frac{1}{125}-\frac{1}{625}\right)}{4.\left(\frac{1}{5}-\frac{1}{25}-\frac{1}{125}-\frac{1}{625}\right)}\)
= \(1+\frac{3}{4}\)
= \(\frac{4}{4}+\frac{3}{4}\)
= \(\frac{7}{4}\)
HỌC TỐT 
a, \(\left(\frac{17}{6}+\frac{13}{9}\right):\left(\frac{121}{12}+\frac{19}{2}\right)\)
\(=\frac{77}{18}:\frac{235}{12}=\frac{77}{18}.\frac{12}{235}=\frac{154}{705}\)
b, \(\left(\frac{19}{2}-\frac{35}{4}\right).\frac{7}{2}+\frac{5}{8}:\frac{5}{3}\)
\(\frac{3}{4}.\frac{7}{2}+\frac{5}{8}.\frac{3}{5}=\frac{21}{8}+\frac{3}{8}=\frac{24}{8}=3\)
c, \(140.\left(\frac{25}{28}+\frac{25}{36}+\frac{5}{9}\right)=140.\frac{10}{7}=200\)
d, \(\left(\frac{7}{5}-\frac{7}{25}+\frac{7}{125}-\frac{7}{625}\right):\left(1-\frac{1}{5}+\frac{1}{25}-\frac{1}{125}\right)\)
\(=\frac{728}{625}:\frac{104}{125}=\frac{728}{625}.\frac{125}{104}=\frac{7}{5}\)
c)=140[(50.10101)/(56.10101)+(50.10101)/(72.10101)+(50.10101)/(90.10101)]
=140(50/56+50/72+50/90)
=140.50(1/56+1/72+1/90)
=7000(1/7.8+1/8.9+1/9.10)
=7000(1/7-1/8+1/8-1/9+1/9-1/10)
=7000(1/7-1/10)
=7000.3/70
=300
Xét hạng tổng quát:
\(\frac{1}{\sqrt{n-1}+\sqrt{n}}=\frac{1}{\sqrt{n}+\sqrt{n-1}}=\frac{\sqrt{n}-\sqrt{n-1}}{n-n+1}=\sqrt{n}-\sqrt{n-1}\)
Áp dụng vào bài, ta có:
\(\frac{1}{1+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+\frac{1}{\sqrt{3}+\sqrt{4}}+\frac{1}{\sqrt{n-1}+\sqrt{n}}\)
\(=\left(\sqrt{2}-1\right)+\left(\sqrt{3}-\sqrt{2}\right)+\left(\sqrt{4}-\sqrt{3}\right)+\left(\sqrt{n}-\sqrt{n-1}\right)\)
\(=\sqrt{n}-1\)
\(\frac{5}{7}\times\frac{1}{3}-\frac{5}{7}\times\frac{1}{4}-\frac{5}{7}\times\frac{1}{2}\)
\(=\frac{5}{7}\times\left(\frac{1}{3}-\frac{1}{4}-\frac{1}{2}\right)\)
\(=\frac{5}{7}\times\left(\frac{4}{12}-\frac{3}{12}-\frac{6}{12}\right)\)
\(=\frac{5}{7}\times\left(\frac{4-3-6}{12}\right)\)
\(=\frac{5}{7}\times\frac{-5}{12}\)
\(=\frac{5\times\left(-5\right)}{7\times12}\)
\(=\frac{-25}{84}\)
\(\frac{5}{7}.\frac{1}{3}-\frac{5}{7}.\frac{1}{4}-\frac{5}{7}.\frac{1}{2}\)
= \(\frac{5}{7}.\left(\frac{1}{3}-\frac{1}{4}-\frac{1}{2}\right).1\)
\(=\frac{5}{7}.\frac{-5}{12}\)
\(=-\frac{25}{84}\)
Lớp 6 làm gì học căn bậc . Mình làm cho bạn nếu lớp khác :
\(\left(\frac{1}{\sqrt{625}}+\frac{1}{5}+1\right):\left(\frac{1}{25}-\frac{1}{\sqrt{25}}-1\right)\)
\(=\left(\frac{1}{25}+\frac{1}{5}+1\right):\left(\frac{1}{25}-\frac{1}{5}-1\right)\)
\(=\frac{31}{25}:\frac{-29}{25}\)
\(=\frac{-31}{29}\)
xl bạn đáng ra là mình làm lớp 7 mak nó thành ra lớp 6