\(\dfrac{2x^2+4x+2}{4x\left(x+1\right)}=\dfrac{2\left(x+1\right)^2}{4x\left(x+1\right)}=\dfrac{x+1}{2x}\).
\(\dfrac{2x^2+4x+2}{4x\left(x+1\right)}=\dfrac{2\left(x^2+2x+1\right)}{4x\left(x+1\right)}=\dfrac{\left(x+1\right)^2}{2x\left(x+1\right)}=\dfrac{x+1}{2x}\)