$\begin{array}{l}\quad\dfrac{1+\dfrac12+\dfrac13+\dfrac14}{1-\dfrac12+\dfrac13-\dfrac14}\div\dfrac{3+\dfrac32+\dfrac33+\dfrac34}{2-\dfrac22+\dfrac23-\dfrac24}\\=\dfrac{1+\dfrac12+\dfrac13+\dfrac14}{1-\dfrac12+\dfrac13-\dfrac14}\div\dfrac{3\cdot\left(1+\dfrac12+\dfrac13+\dfrac14\right)}{2\cdot\left(1-\dfrac12+\dfrac13-\dfrac14\right)}\\=\dfrac{\left(1+\dfrac12+\dfrac13+\dfrac14\right)\cdot2\cdot\left(1-\dfrac12+\dfrac13-\dfrac14\right)}{\left(1-\dfrac12+\dfrac13-\dfrac14\right)\cdot3\cdot\left(1+\dfrac12+\dfrac13+\dfrac14\right)}\\=\dfrac23 \end{array}$