\(\dfrac{3x}{x^2+x+1}=\dfrac{3x\left(x-1\right)}{\left(x^2+x+1\right)\left(x-1\right)}\)
\(\dfrac{7}{x-1}=\dfrac{7x^2+7x+7}{\left(x-1\right)\left(x^2+x+1\right)}\)
\(\dfrac{6x^2-5x+11}{x^3-1}=\dfrac{6x^2-5x+11}{\left(x-1\right)\left(x^2+x+1\right)}\)