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\(...=-\dfrac{4}{7}-\dfrac{3}{11}+\dfrac{3}{11}-\dfrac{3}{7}=-\dfrac{4}{7}-\dfrac{3}{7}=-1\)
-(4/7 + 3/11) - (-3/11 + 3/7)
= (-4/7) + (-3/11) - (-3/11) - 3/7
= [(-4/7) - 3/7)] + [(-3/11) - (-3/11)]
= -1 + 0
= -1
Đặt \(A=1992\cdot19911991-1991\cdot19921992\)
\(\Rightarrow A=1992\cdot\left(1991\cdot10001\right)-1991\cdot\left(1992\cdot10001\right)\)
\(\Rightarrow A=1992\cdot1991\cdot10001-1991\cdot1992\cdot10001=0\)
\(=\dfrac{2011}{2012}\cdot\left(3-3-\dfrac{2011}{2012}\right)-\dfrac{1}{2012}\cdot\dfrac{2011}{2012}\)
\(=\dfrac{2011}{2012}\cdot\left(-\dfrac{2011}{2012}\right)-\dfrac{1}{2012}\cdot\dfrac{2011}{2012}\)
\(=\dfrac{2011}{2012}\cdot\left(\dfrac{-2011}{2012}-\dfrac{1}{2012}\right)\)
\(=\dfrac{2011}{2012}\cdot\left(-1\right)\)
\(=-\dfrac{2011}{2012}\)
\(B=\dfrac{\dfrac{5-10\sqrt{2}+6\sqrt{2}}{70}\cdot\left(-\dfrac{4}{15}\right)}{\dfrac{5+6\sqrt{2}-10\sqrt{2}}{50}\cdot\dfrac{5}{7}}=\dfrac{10-8\sqrt{2}}{525}:\dfrac{5-4\sqrt{2}}{70}\\ B=\dfrac{2\left(5-4\sqrt{2}\right)}{525}\cdot\dfrac{70}{5-4\sqrt{2}}=\dfrac{4}{15}\)
`@` `\text {Ans}`
`\downarrow`
`b)`
`12/11 + 7/15*9/22 - (-8)/15*9/22`
`= 12/11+ 9/22*(7/15 - (-8)/15)`
`=12/11 + 9/22*(7/15+8/15)`
`= 12/11+ 9/22*15/15`
`= 12/11 + 9/22*1`
`= 12/11+9/22`
`= 24/22 + 9/22`
`= 33/22`
`= 3/2`
\(\dfrac{12}{11}+\dfrac{7}{15}\cdot\dfrac{9}{22}-\dfrac{-8}{15}\cdot\dfrac{9}{22}\)
\(=\dfrac{12}{11}+\dfrac{9}{22}\cdot\left(\dfrac{7}{15}-\dfrac{-8}{15}\right)\)
\(=\dfrac{12}{11}+\dfrac{9}{22}\cdot\dfrac{15}{15}\)
\(=\dfrac{12}{11}+\dfrac{9}{22}\)
\(=\dfrac{24}{22}+\dfrac{9}{22}\)
\(=\dfrac{33}{22}\)
\(=\dfrac{3}{2}\)
tính nhanh