a: \(=\dfrac{4x^2-5x+1}{\left(x-1\right)\left(x^2+x+1\right)}+\dfrac{4x^2+x+19}{\left(x-1\right)\left(x^2+x+1\right)}-\dfrac{8x^2+8x+8}{\left(x-1\right)\left(x^2+x+1\right)}\)
\(=\dfrac{8x^2-4x+20-8x^2-8x-8}{\left(x-1\right)\left(x^2+x+1\right)}=\dfrac{-12x+12}{\left(x-1\right)\left(x^2+x+1\right)}=\dfrac{-12}{x^2+x+1}\)
b: Thay x=1/2 vào A, ta được:
\(A=\dfrac{-12}{\dfrac{1}{4}+\dfrac{1}{2}+1}=-\dfrac{12}{\dfrac{7}{4}}=-21\)
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