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`3/4+2/5+3/12`
`=3/4+3/12+2/5`
`=9/12+3/12+2/5`
`=12/12+2/5`
`=1+2/5`
`=7/5`
\(=\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}\)
\(=\dfrac{1}{2}-\dfrac{1}{6}\)
\(=\dfrac{1}{3}\)
\(\dfrac{4}{7}x\left(\dfrac{2}{5}+\dfrac{3}{5}\right)=\dfrac{4}{7}x1=\dfrac{4}{7}\)
\(=\dfrac{3}{7}\left(\dfrac{5}{4}-\dfrac{2}{9}\right)=\dfrac{3}{7}\cdot\dfrac{45-8}{36}=\dfrac{3}{36}\cdot\dfrac{37}{7}=\dfrac{37}{84}\)
\(\dfrac{3}{7}:\dfrac{4}{5}-\dfrac{3}{7}:\dfrac{9}{2}\)
\(=\dfrac{3}{7}\times\dfrac{5}{4}-\dfrac{3}{7}\times\dfrac{2}{9}\)
\(=\dfrac{3}{7}\times\left(\dfrac{5}{4}-\dfrac{2}{9}\right)\)
\(=\dfrac{3}{7}\times\left(\dfrac{45}{36}-\dfrac{8}{36}\right)\)
\(=\dfrac{3}{7}\times\dfrac{37}{36}\)
\(=\dfrac{37}{84}\)
#DatNe
`1/(2*3)+1/(3*4)+1/(4*5)+...+1/(9*10)`
`=1/2-1/3+1/3-1/4+1/4-1/5+...+1/9-1/10`
`=1/2-1/10`
`=5/10-1/10`
`=4/10=2/5`
\(\dfrac{2}{3}\times\dfrac{3}{4}\times\dfrac{4}{5}\) \(=\dfrac{2\times3\times4}{3\times4\times5}\) \(=\) \(\dfrac{2}{5}\)
`5/9xx1/4+4/9xx3/12`
`=5/9xx1/4+4/9xx1/4`
`=1/4xx(5/9+4/9)`
`=1/4xx9/9`
`=1/4xx1`
`=1/4`