\(\left(\dfrac{x+2}{x+1}-\dfrac{2x}{x-1}\right)\cdot\dfrac{3x+3}{x+4x^2}+\dfrac{x+7}{x^2-x}\)
\(=\dfrac{x^2+x-2-2x^2-2x}{\left(x-1\right)\left(x+1\right)}\cdot\dfrac{3\left(x+1\right)}{x\left(4x+1\right)}+\dfrac{x+7}{x\left(x-1\right)}\)
\(=\dfrac{-x^2-x-2}{\left(x-1\right)}\cdot\dfrac{3}{x\left(4x+1\right)}+\dfrac{x+7}{x\left(x-1\right)}\)
\(=\dfrac{-3x^2-3x-6+4x^2+28x+x+7}{x\left(4x+1\right)\left(x-1\right)}\)
\(=\dfrac{x^2+26x+1}{x\left(4x+1\right)\left(x-1\right)}\)
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