Question

Tìm x:

\(\dfrac{2}{\left(x-1\right)\left(x-3\right)}\)\(+\dfrac{5}{\left(x-3\right)\left(x-8\right)}\)\(+\dfrac{12}{\left(x-8\right)\left(x-20\right)}\)\(-\dfrac{1}{x-20}=\dfrac{-3}{4}\)

Answer 1

\(\dfrac{2}{\left(x-1\right)\left(x-3\right)}+\dfrac{5}{\left(x-3\right)\left(x-8\right)}+\dfrac{12}{\left(x-8\right)\left(x-20\right)}+\dfrac{1}{x-20}=\dfrac{3}{4}\)

\(\Rightarrow\dfrac{x}{x-1}-\dfrac{1}{x-3}+\dfrac{1}{x-3}-\dfrac{1}{x-8}+\dfrac{1}{x-8}-\dfrac{1}{x-20}+\dfrac{1}{x-20}=\dfrac{3}{4}\)

\(\Rightarrow\dfrac{1}{x-1}=\dfrac{3}{4}\Rightarrow3x-3=4\Rightarrow x=\dfrac{7}{3}\)

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