I am having difficulty understanding how to deal with the big O term in the denominator of a fraction while reading a paper.
The form of the fraction is given by $$\frac{a+ b h^k + O(h^{k+2})}{c + d h^k + O(h^{k+2})}$$ and the result is given as $\frac{a+b h^k}{c + d h^k} + O(h^{2k})$.
How do we get rid of the $O(h^{k+2})$ terms each in the numerator and the denominator and take them out as a term $O(h^{2k})$? I would greatly appreciate any help.