\(=\dfrac{x^3+x^2+x^2+x}{x^2+x}\\ =\dfrac{x^2\left(x+1\right)+x\left(x+1\right)}{x\left(x+1\right)}\\ =\dfrac{\left(x+1\right)\left(x^2+x\right)}{x\left(x+1\right)}\\ =\dfrac{x\left(x+1\right)\left(x+1\right)}{x\left(x+1\right)}\\ =x+1\)
\(\dfrac{x^3+2x^2+x}{x^2+x}\\ =\dfrac{x^3+x^2+x^2+x}{x\left(x+1\right)}\\ =\dfrac{x^2\left(x+1\right)+x\left(x+1\right)}{x\left(x+1\right)}\\ =\dfrac{\left(x^2+x\right)\left(x+1\right)}{x\left(x+1\right)}\\ =\dfrac{x\left(x+1\right)}{x}\\ =x+1\)
=x(x^2+2x+1)/x(x+1)=(x+1)^2/(x+1)=x+1
