a: \(B=\dfrac{-a^4+a^3+a-1}{a^4+a^3+3a^2+2a+2}\)
\(=\dfrac{-a^3\left(a-1\right)+\left(a-1\right)}{a^4+a^3+a^2+2a^2+2a+2}\)
\(=\dfrac{-\left(a-1\right)^2\left(a^2+a+1\right)}{\left(a^2+a+1\right)\left(a+2\right)}\)
\(=\dfrac{-\left(a-1\right)^2}{a+2}\)
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