first off, I'd like for the sake of clarification to indicate we're assuming there's an error in the process above and so hmmm what is it?

now, let's notice, somehow 9/25 came out of the blue, but the assumption being that we had 1/5, well, hell we'll split it in two pieces, +9/25 and -9/25 that way we can send one of them over and look like the equation on the right end, hmmm but is 9/5 - 9/5 really equals to 1/5?

now we can say, well, hmmm the 9/25's came from the zero, ok, cool, we can use them, but what the heck happened to the 1/5? thus the error.