Is it possible to factor the risk ratio from this equation?

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I have this weighted risk ratio equation here: $$\frac{a(b/e+d/f)}{b(a/g+c/h)}$$

I am interested in factoring this out of the equation, i.e. the unweighted risk ratio: $$\frac{a(b+d)}{b(a+c)}$$

Is this at all possible?

Thank you!

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Of course the weighted version can't be equal to the unweighted version in general.

To reduce to the unweighted version, set the weight to be $e=f=g=h$.