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a) https://hoc247.net/hoi-dap/toan-7/thuc-hien-phep-tinh-5-5-27-7-23-0-5-5-27-16-23-faq218258.html
b) https://hoidap247.com/cau-hoi/1507941
\(\dfrac{1}{3}-\dfrac{3}{5}+\dfrac{5}{7}-\dfrac{7}{9}+\dfrac{9}{11}-\dfrac{11}{13}+\dfrac{13}{15}+\dfrac{11}{13}-\dfrac{9}{11}+\dfrac{7}{9}-\dfrac{5}{7}+\dfrac{3}{5}-\dfrac{1}{3}\)
\(=\left(\dfrac{1}{3}-\dfrac{1}{3}\right)-\left(\dfrac{3}{5}-\dfrac{3}{5}\right)+\left(\dfrac{5}{7}-\dfrac{5}{7}\right)-\left(\dfrac{7}{9}-\dfrac{7}{9}\right)+\left(\dfrac{9}{11}-\dfrac{9}{11}\right)-\left(\dfrac{11}{13}-\dfrac{11}{13}\right)+\dfrac{13}{15}\)
\(=\dfrac{13}{15}\)
\(\left(x:2,2\right)\times\dfrac{1}{6}=\dfrac{-3}{8}\times\left(0,5-1\dfrac{3}{5}\right)\)
\(\Rightarrow\left(x:2,2\right)\times\dfrac{1}{6}=\dfrac{-3}{8}\times\left(\dfrac{1}{2}-\dfrac{8}{5}\right)\)
\(\Rightarrow\left(x:2,2\right)\times\dfrac{1}{6}=\dfrac{-3}{8}\times\dfrac{11}{10}\)
\(\Rightarrow\left(x:2,2\right)\times\dfrac{1}{6}=\dfrac{33}{80}\)
\(\Rightarrow x:2,2=\dfrac{33}{80}:\dfrac{1}{6}\)
\(\Rightarrow x:2,2=\dfrac{99}{40}\)
\(\Rightarrow x=\dfrac{99}{40}\times2,2\)
\(\Rightarrow x=\dfrac{1089}{200}\)
=>(x:2,2)*1/6=-3/8(1/2-8/5)=33/80
=>x:2,2=99/40
=>x=1089/200
\(\Rightarrow\dfrac{5}{7}-x=-\dfrac{1}{5}\Rightarrow x=\dfrac{32}{35}\)
Có: \(\dfrac{\left(-3\right)^{10}x15^5}{25^3x\left(-9\right)^7}=\dfrac{3^{10}.\left(3.5\right)^5x}{-\left(3^2\right)^7\left(5^2\right)^3x}\)
\(=\dfrac{3^{15}.5^5x}{-3^{14}.5^6x}\)\(=\dfrac{3^{14}.5^5\left(3x\right)}{3^{14}.5^5\left(-5x\right)}=\dfrac{3x}{-5x}=-\dfrac{3}{5}\)
Vậy...
Đặt : \(\dfrac{x}{5}=\dfrac{y}{3}=k\)
`=>x=5k,y=3k`
Ta có : \(x^2-y^2=4=>\left(5k\right)^2-\left(3k\right)^2=4\\ =>25k^2-9k^2=4\\ =>16k^2=4\\ =>k^2=\dfrac{1}{4}\\ =>k=\pm\dfrac{1}{2}\)
\(=>\left[{}\begin{matrix}\left\{{}\begin{matrix}x=\dfrac{5}{2}\\y=\dfrac{3}{2}\end{matrix}\right.\\\left\{{}\begin{matrix}x=-\dfrac{5}{2}\\y=-\dfrac{3}{2}\end{matrix}\right.\end{matrix}\right.\)
\(\dfrac{3}{5}\)\(x\) - \(\dfrac{11}{5}\) = \(\dfrac{-3}{14}\) : \(\dfrac{5}{7}\)
\(\dfrac{3}{5}\)\(x\) - \(\dfrac{11}{5}\) = - \(\dfrac{3}{10}\)
\(\dfrac{3}{5}\)\(x\) = - \(\dfrac{3}{10}\) + \(\dfrac{11}{5}\)
\(\dfrac{3}{5}\)\(x\) = \(\dfrac{19}{10}\)
\(x\) = \(\dfrac{19}{10}\) : \(\dfrac{3}{5}\)
\(x\) = \(\dfrac{19}{6}\)
\(\dfrac{3}{5}x-\dfrac{11}{5}=-\dfrac{3}{14}:\dfrac{5}{7}\)
\(\Rightarrow\dfrac{3}{5}x-\dfrac{11}{5}=-\dfrac{3}{14}\cdot\dfrac{7}{5}\)
\(\Rightarrow\dfrac{3}{5}x-\dfrac{11}{5}=-\dfrac{3}{10}\)
\(\Rightarrow\dfrac{3}{5}x=-\dfrac{3}{10}+\dfrac{11}{5}\)
\(\Rightarrow\dfrac{3}{5}x=\dfrac{19}{10}\)
\(\Rightarrow x=\dfrac{19}{10}:\dfrac{3}{5}\)
\(\Rightarrow x=\dfrac{19}{6}\)