Ratio - division by zero

I am working with some data and I was hoping to look at the change in one variable as a ratio of the change in another variable (both have been standardized so that they can be compared) however, in some cases the change in these variables is zero and thus it would result in me trying to divide by zero. Is there a neat way around this problem. I have thought about various transformations but I am needing to derive some kind of ratio value?
Well I've changed my method a bit now and am looking at the ratio between the change of the two variables as proportions of their original values:

For example ((A1 - A2)./A1)./((B1 - B2)./B1)

But as I say because the B variable (and in some cases the A variable) doesnt change at all over the time period then I am left with this problem when defining a ratio