When I was looking through p23-24 of Symmetry Analysis of Differential Equations by Daniel J. Arrigo, I wasn’t sure why we can do this: $$\frac{\frac{dy}{dx} + [Y_x+Y_yy’]\epsilon+O(\epsilon^2) }{1+[X_x+X_yy’]\epsilon+O(\epsilon^2)}=(\frac{dy}{dx} + [Y_x+Y_yy’]\epsilon+O(\epsilon^2))( 1-[X_x+X_yy’]\epsilon+O(\epsilon^2)) $$
Can anyone explain why we can do this in the intermediate step?