Problem of finding best combination of features when desired feature is feature some_feature_A/some_feature_B
In theory, I think a deep neural net might be able to find features that are the product of two other columns.  There exist some nice mathematical results which guarantee the ability of a neural net (with certain activation functions) to approximate any function, so there's no theoretical reason why a neural net couldn't compute the division function $f(x, y) = \frac{x}{y}$.  That being said, it may be difficult to achieve in practice without a little preprocessing.

If you want to give it a try, I would suggest adding additional features obtained by taking the logarithm of any numerical features in the dataset.  This might make it easier for the network for learn features that are products of other features (since $\log{(x * y)} = \log{x} + \log{y}$ and $\log{x / y} = \log{x} - \log{y}$).