2/3 + 3/5 =? giúp mình với
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\(\dfrac{2}{1.3}+\dfrac{2}{3.5}+\dfrac{2}{5.7}+...+\dfrac{2}{99.101}=1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{99}-\dfrac{1}{101}=1-\dfrac{1}{101}=\dfrac{100}{101}\)
\(\dfrac{2}{1\cdot3}+\dfrac{2}{3\cdot5}+\dfrac{2}{5\cdot7}+...+\dfrac{2}{99\cdot101}\\ =1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{99}-\dfrac{1}{101}\\ =1-\dfrac{1}{101}=\dfrac{100}{101}\)
\(\dfrac{3}{2}\)(\(x\) - \(\dfrac{5}{3}\)) - \(\dfrac{4}{5}\) = \(x\) + 1
\(\dfrac{3}{2}\) \(x\) - \(\dfrac{15}{6}\) - \(\dfrac{4}{5}\) = \(x\) + 1
\(\dfrac{3}{2}\)\(x\) - \(x\) = 1 + \(\dfrac{15}{6}\) + \(\dfrac{4}{5}\)
\(\dfrac{1}{2}\)\(x\) =\(\dfrac{43}{10}\)
\(x\) = \(\dfrac{43}{10}\) \(\times\) 2
\(x\) = \(\dfrac{43}{5}\)
\(\dfrac{3}{2}\left(x-\dfrac{5}{3}\right)-\dfrac{4}{5}=x+1\\ \Rightarrow\dfrac{3.\left(x-\dfrac{5}{3}\right)}{2}-\dfrac{4}{5}=x+1\\ \Rightarrow\dfrac{3x-5}{2}-\dfrac{4}{5}=x+1\Rightarrow\dfrac{5\left(3x-5\right)}{10}-\dfrac{8}{10}=x+1\\ \Rightarrow\dfrac{15x-33}{10}=x+1\\ \Rightarrow\dfrac{15x-33}{10}-x=x+1\\ \Rightarrow\dfrac{15x-33}{10}=x+1-x\\ \Rightarrow5x-33=10\\ \Rightarrow5x=10+33\\\Rightarrow5x=43\\ \Rightarrow x=\dfrac{43}{5} \)
-5/13+2/5+-8/13+3/5-3/7
=(-5/13 + -8/13) +(2/5+3/5)-3/7
= -13/13 + 5/5 -3/7
=-1 + 1 -3/7
=-3/7
\(\left(\dfrac{6}{5}-2,4\right):\dfrac{-3}{5}-\dfrac{3}{2}.\left(1\dfrac{1}{2}:\dfrac{1}{2}\right)\)
= \(\dfrac{-6}{5}\): \(\dfrac{-3}{5}-\dfrac{3}{2}.\left(\dfrac{3}{2}:\dfrac{1}{2}\right)\)
= \(\dfrac{-5}{2}\)
\(\left(\dfrac{6}{5}-2,4\right):\left(-3,5\right)-\dfrac{3}{2}.\left(1\dfrac{1}{2}:\dfrac{1}{2}\right)=-\dfrac{6}{5}:\left(-\dfrac{7}{2}\right)-\dfrac{3}{2}.3=\dfrac{12}{35}-3=-\dfrac{93}{35}\)
\(\frac{4}{5}\left(15+\frac{2}{3}\right)-\frac{4}{5}\left(20+\frac{2}{3}\right)\)
\(=\frac{4}{5}\left[\left(15+\frac{2}{3}\right)-\left(20+\frac{2}{3}\right)\right]\)
\(=\frac{4}{5}.\left(15+\frac{2}{3}-20-\frac{2}{3}\right)\)
\(=\frac{4}{5}.\left(-5\right)\)
\(=-4\)
19/15
2/3+3/5
=19/15 nha
HT