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Áp dụng bất đẳng thức : \(\frac{a}{b}< 1\Rightarrow\frac{a}{b}< \frac{a+n}{b+n}\)
Ta chứng minh được \(\frac{20}{39}>\frac{18}{41};\frac{18}{43}>\frac{14}{39};\frac{22}{27}>\frac{22}{29}\)
\(\Rightarrow\frac{20}{39}+\frac{22}{27}+\frac{18}{43}>\frac{14}{37}+\frac{22}{29}+\frac{18}{41}\)
\(\Rightarrow A>B\)
\(\left(4\frac{5}{37}-3\frac{4}{5}+8\frac{15}{29}\right)-\left(3\frac{5}{37}-6\frac{14}{29}\right)\)
\(\left(4\frac{5}{37}-3\frac{4}{5}+8\frac{15}{29}\right)-\left(3\frac{5}{37}-6\frac{14}{29}\right)\)
a ) Ta có
\(\frac{29}{33}>\frac{29}{37}\)( đồng tử khác mẫu )
\(\frac{22}{37}< \frac{29}{37}\)( đồng mẫu khác tử )
=> \(\frac{29}{33}>\frac{29}{37}>\frac{22}{37}\)
b ) \(\frac{163}{257}< \frac{163}{221}\)
\(\frac{162}{257}>\frac{149}{257}\)
\(\Rightarrow\frac{163}{221}>\frac{163}{257}>\frac{149}{257}\)
a) ta có: \(\frac{22}{37}< \frac{29}{37}\)
\(\frac{29}{33}>\frac{29}{37}\)
\(\Rightarrow\frac{22}{37}< \frac{29}{37}< \frac{29}{33}\)
b) ta có: \(\frac{163}{257}>\frac{149}{257}\)
\(\frac{163}{221}>\frac{163}{257}\)
\(\Rightarrow\frac{163}{221}>\frac{163}{257}>\frac{149}{257}\)
Đặt \(A=\frac{9+\frac{9}{11}+\frac{18}{23}-\frac{27}{37}}{8+\frac{8}{11}+\frac{16}{23}-\frac{24}{37}}-\frac{2+\frac{16}{29}-\frac{24}{13}-\frac{32}{11}}{3+\frac{24}{29}-\frac{36}{13}-\frac{48}{11}}\)\(=\frac{9\left(1+\frac{1}{11}+\frac{2}{23}-\frac{3}{37}\right)}{8\left(1+\frac{1}{11}+\frac{2}{23}-\frac{3}{37}\right)}-\frac{2\left(1+\frac{8}{29}-\frac{12}{13}-\frac{16}{11}\right)}{3\left(1+\frac{8}{29}-\frac{12}{13}-\frac{16}{11}\right)}\)
\(=\frac{9}{8}-\frac{2}{3}\)(do \(1+\frac{1}{11}+\frac{2}{23}-\frac{3}{37};1+\frac{8}{29}-\frac{12}{13}-\frac{16}{11}\ne0\))
\(=\frac{27}{24}-\frac{16}{24}=\frac{11}{24}.\)
Vậy A = \(\frac{11}{24}.\)
22/37<29/37
29/37<29/33
Vậy 22/37<29/37<29/33
Ta có 22/37 < 29/37 và 29/37 < 29/33
=> 22/37< 29/37 < 29/33