1960 AHSME Problem 28

The equation x-\frac{7}{x-3}=3-\frac{7}{x-3} has:

\textbf{(A)}\ \text{infinitely many integral roots}\qquad\textbf{(B)}\ \text{no root}\qquad\textbf{(C)}\ \text{one integral root}\qquad \textbf{(D)}\ \text{two equal integral roots}\qquad\textbf{(E)}\ \text{two equal non-integral roots}

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