\(\dfrac{1}{x^2-x+1}+\dfrac{1-x^2}{x^3+1}\)
\(=\dfrac{1}{x^2-x+1}+\dfrac{1-x^2}{\left(x+1\right)\left(x^2-x+1\right)}\) MTC: \(\left(x+1\right)\left(x^2-x+1\right)\)
\(=\dfrac{x+1}{\left(x+1\right)\left(x^2-x+1\right)}+\dfrac{1-x^2}{\left(x+1\right)\left(x^2-x+1\right)}\)
\(=\dfrac{x+1+1-x^2}{\left(x+1\right)\left(x^2-x+1\right)}\)
\(=\dfrac{\left(x+1\right)+\left(1-x^2\right)}{\left(x+1\right)\left(x^2-x+1\right)}\)
\(=\dfrac{\left(x+1\right)-\left(x^2-1\right)}{\left(x+1\right)\left(x^2-x+1\right)}\)
\(=\dfrac{\left(x+1\right)-\left(x-1\right)\left(x+1\right)}{\left(x+1\right)\left(x^2-x+1\right)}\)
\(=\dfrac{\left(x+1\right)\left(1-x+1\right)}{\left(x+1\right)\left(x^2-x+1\right)}\)
\(=\dfrac{2-x}{x^2-x+1}\)
