\(ĐK:x\ne\dfrac{1}{2};x\ne1;x\ne\dfrac{3}{2};x\ne2;x\ne\dfrac{5}{2}\\ PT\Leftrightarrow\dfrac{1}{\left(2x-1\right)\left(x-1\right)}+\dfrac{1}{\left(x-1\right)\left(3x-2\right)}+\dfrac{1}{\left(3x-2\right)\left(x-2\right)}+\dfrac{1}{\left(x-2\right)\left(5x-2\right)}=\dfrac{4}{21}\\ \Leftrightarrow2\left[\dfrac{\dfrac{1}{2}}{\left(x-\dfrac{1}{2}\right)\left(x-1\right)}+\dfrac{\dfrac{1}{2}}{\left(x-1\right)\left(x-\dfrac{3}{2}\right)}+\dfrac{\dfrac{1}{2}}{\left(x-\dfrac{3}{2}\right)\left(x-2\right)}+\dfrac{\dfrac{1}{2}}{\left(x-2\right)\left(x-\dfrac{5}{2}\right)}\right]=\dfrac{4}{21}\)

\(\Leftrightarrow\dfrac{1}{x-1}-\dfrac{1}{x-\dfrac{1}{2}}+\dfrac{1}{x-\dfrac{3}{2}}-\dfrac{1}{x-1}+\dfrac{1}{x-2}-\dfrac{1}{x-\dfrac{3}{2}}+\dfrac{1}{x-\dfrac{5}{2}}-\dfrac{1}{x-2}=\dfrac{2}{21}\\ \Leftrightarrow\dfrac{1}{x-1}-\dfrac{1}{x-\dfrac{5}{2}}=\dfrac{2}{21}\\ \Leftrightarrow\dfrac{x-\dfrac{5}{2}-x+1}{\left(x-1\right)\left(x-\dfrac{5}{2}\right)}=\dfrac{2}{21}\\ \Leftrightarrow\dfrac{-\dfrac{3}{2}}{x^2-\dfrac{7}{2}x+\dfrac{5}{2}}=\dfrac{2}{21}\\ \Leftrightarrow x^2-\dfrac{7}{2}x+\dfrac{5}{2}=-\dfrac{63}{4}\\ \Leftrightarrow4x^2-14x+10=-63\\ \Leftrightarrow4x^2-14x+73=0\\ \Leftrightarrow x\in\varnothing\)

b d a d b

a c b d a c

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c c d d a

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19 d

20 d

21 b

22 c

23 a

24 c

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9 d

10 b

11 d

12 b

13c

14 c