  Gate-voltage control of inter-edge tunneling at a split-gate constriction in
the fractional quantum Hall regime is reported. Quantitative agreement with the
behavior predicted for out-of-equilibrium quasiparticle transport between
chiral Luttinger liquids is shown at low temperatures at specific values of the
backscattering strength. When the latter is lowered by changing the gate
voltage the zero-bias peak of the tunneling conductance evolves into a minimum
and a non-linear quasihole-like characteristic emerges. Our analysis emphasizes
the role of the local filling factor in the split-gate constriction region.
