Two independent random variables X and Y have corresponding probability generating functions:

G_x(t) = e^{3(t – 1)}

and

G_y(t) = e^{t(t – 1)}

It is given that A = Y - X.

a. A student made the following attempt to find G_A(t):

Step I: G_x+y(t) = G_x(t) × G_y(t)

Step 2: Therefore G_y-x(t) = G_y(t) ÷ G_x(t)

Step 3: G_y-x(t) = e^{5(t – 1)} ÷ e^{3(t – 1)}

Step 4: G_y-x(t) = e^2(t-1)

Which step contains the error in the student's working? 

b. Find the correct probability generating function of A, G_A(t).