1967 AHSME Problem 34

Points D, E, F are taken respectively on sides AB, BC, and CA of triangle ABC so that AD:DB=BE:CE=CF:FA=1:n. The ratio of the area of triangle DEF to that of triangle ABC is:

\textbf{(A)}\ \frac{n^2-n+1}{(n+1)^2}\qquad \textbf{(B)}\ \frac{1}{(n+1)^2}\qquad \textbf{(C)}\ \frac{2n^2}{(n+1)^2}\qquad \textbf{(D)}\ \frac{n^2}{(n+1)^2}\qquad \textbf{(E)}\ \frac{n(n-1)}{n+1}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.