Why there is a sign change when not writing in long division?

Question

I have a question about understanding how this step $$ \int_0^{\delta/\epsilon}\frac{du}{1+u+\epsilon^2u^3/3+O(\epsilon^4u^5)} $$ becomes $$ \int_0^{\delta/\epsilon}\frac{du}{1+u}\left(1-\frac{\epsilon^2}{3}\frac{u^3}{1+u}+O(\epsilon^4u^4)\right) $$ It makes sense to me to rewrite the first equation as $$ \int_0^{\delta/\epsilon}\frac{du}{(1+u)\left[1+\epsilon^2u^3/3(1+u)+O(\epsilon^4u^5)\right]} $$ Why did the sign on the second term of $\left[1+\epsilon^2u^3/3(1+u)+O(\epsilon^4u^5)\right]$ becomes minus in the final result? Which identities are used? Thanks for the help!