\(\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+\dfrac{1}{5.6}=\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}=\dfrac{1}{2}-\dfrac{1}{6}=\dfrac{4}{12}=\dfrac{1}{3}\)

\(xy+x-y=x\left(y+1\right)-y=4\)
\(x\left(y+1\right)-y-1=3\)
\(x\left(y+1\right)-\left(y+1\right)=3\)
\(\left(x-1\right)\left(y+1\right)=3\)
\(=>\left[{}\begin{matrix}x-1=1\\x-1=-1\\x-1=3\\x-1=-3\end{matrix}\right.=>\left[{}\begin{matrix}y+1=3\\y+1=-3\\y+1=1\\y+1=-1\end{matrix}\right.\)
\(=>\left[{}\begin{matrix}x=2\\x=0\\x=4\\x=-2\end{matrix}\right.=>\left[{}\begin{matrix}y=2\\y=-4\\y=0\\y=-2\end{matrix}\right.\)

C

A. \(\dfrac{12}{13}\times\dfrac{5}{9}+\dfrac{12}{13}\times\dfrac{13}{9}=\dfrac{12}{13}\times\left(\dfrac{5}{9}+\dfrac{13}{9}\right)=\dfrac{12}{13}\times2=\dfrac{24}{13}\)
B.\(\dfrac{29}{12}:\dfrac{1}{2}-\dfrac{5}{12}:\dfrac{1}{2}=\left(\dfrac{29}{12}-\dfrac{5}{12}\right):\dfrac{1}{2}=2:\dfrac{1}{2}=4\)
C.\(\dfrac{6}{7}\times\dfrac{4}{13}\times\dfrac{7}{6}\times\dfrac{13}{8}=\dfrac{6}{7}\times\dfrac{7}{6}\times\dfrac{4}{13}\times\dfrac{13}{8}=\dfrac{1}{2}\)
D.\(\dfrac{17}{15}-\left(\dfrac{3}{7}+\dfrac{2}{15}\right)=\dfrac{17}{15}-\dfrac{3}{7}-\dfrac{2}{15}=1-\dfrac{3}{7}=\dfrac{4}{7}\)

\(x-\dfrac{5}{7}=\dfrac{3}{5}.\dfrac{1}{2}\)

\(x-\dfrac{5}{7}=\dfrac{3}{10}\)
\(x=\dfrac{3}{10}+\dfrac{5}{7}=\dfrac{71}{70}\)

1 cốc trà

\(y+\dfrac{4}{5}=\dfrac{4}{5}-\left(\dfrac{3}{7}+\dfrac{3}{5}\right)\)
\(y=\dfrac{4}{5}-\left(\dfrac{3}{7}+\dfrac{3}{5}\right)-\dfrac{4}{5}\)
\(y=\dfrac{36}{35}\)

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