I know the correlation of two variables Corr(k,1/a), Corr(k,1/(a+b)).

How can I calculate Corr(k, (1/(1-(b/a)))?

Also, if the two known correlations [Corr(k,1/a), Corr(k,1/(a+b)).] are very high, will it be wrong to assume the correlation I want to estimate [Corr(k, (1/(1-(b/a)))] would also be high?