\(\left\{{}\begin{matrix}\dfrac{x}{x^3+1}=\dfrac{x}{\left(x+1\right)\left(x^2-x+1\right)}=\dfrac{x^2}{x\left(x+1\right)\left(x^2-x+1\right)}\\\dfrac{x+1}{x^2+x}=\dfrac{x+1}{x\left(x+1\right)}=\dfrac{1}{x}=\dfrac{x^3+1}{x\left(x+1\right)\left(x^2-x+1\right)}\\\dfrac{x+2}{x^2-x+1}=\dfrac{x\left(x+1\right)\left(x+2\right)}{x\left(x+1\right)\left(x^2-x+1\right)}=\dfrac{x^3+3x^2+2x}{x\left(x+1\right)\left(x^2-x+1\right)}\end{matrix}\right.\)
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