Question

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

Answer 1

\(\Leftrightarrow\dfrac{2}{x-3}-\dfrac{2}{x-2}+\dfrac{1}{x-8}-\dfrac{1}{x-3}+\dfrac{1}{x-20}-\dfrac{1}{x-8}-\dfrac{1}{x-20}=\dfrac{-3}{4}\)

\(\Leftrightarrow\dfrac{1}{x-3}-\dfrac{2}{x-2}=\dfrac{-3}{4}\)

\(\Leftrightarrow4\left(x-2\right)-8\left(x-3\right)=-3\left(x-3\right)\left(x-2\right)\)

\(\Leftrightarrow4x-8-8x+24+3\left(x^2-5x+6\right)=0\)

\(\Leftrightarrow3x^2-15x+18-4x+16=0\)

\(\Leftrightarrow3x^2-19x+34=0\)

\(\text{Δ}=\left(-19\right)^2-4\cdot3\cdot34=-47< 0\)

Do đó: Phương trình vô nghiệm