Question 34Points $D,$ $E,$ $F$ are taken respectively on sides $AB,$ $BC,$ and $CA$ of triangle $ABC$ so that $AD:DB=1:n,$ $BE:CE=1:n,$ and $CF:FA=1:n.$ The ratio of the area of triangle $DEF$ to that of triangle $ABC$ is:$\dfrac{n^2-n+1}{(n+1)^2}$$\dfrac1{(n+1)^2}$$\dfrac{2n^3}{(n+1)^2}$$\dfrac{n^3}{(n+1)^2}$$\dfrac{n(n-1)}{n+1}$