Completely monotonic ratios of basic and ordinary gamma functions

We investigate conditions for logarithmic complete monotonicity of product ratios gamma and q-gamma functions whose arguments are linear the variable. give necessary sufficient in terms nonnegativity a certain explicitly written measure q case elementary function classical $$q=1$$ case. In latter we further provide simple new leading to many examples logarithmically completely monotonic ratios. Finally, apply some our results study rational functions.