<image>Place 6 small rectangular pieces of paper (as shown in Figure 1) in a non-overlapping manner inside the rectangle ABCD as shown in Figure 2. The uncovered portion exactly divides into two rectangles, with areas of \( S_{1} \) and \( S_{2} \) respectively. Given that the small rectangular pieces have a length of \( a \) and a width of \( b \), with \( a > b \). 

When the length of \( AB \) remains unchanged while the length of \( BC \) increases, if the 6 small rectangular pieces are placed in the same manner inside the new rectangle ABCD, the difference between \( S_{1} \) and \( S_{2} \) always remains unchanged. 

Find the relationship between \( a \) and \( b \).

(1) To solve the above problem, as shown in Figure 3, Xiao Ming sets \( EF = x \), then we can represent \( S_{1} = \) ______ and \( S_{2} = \) ______ ;
(2) Find the relationship between \( a \) and \( b \), and write out the derivation process.
