  The projected gravitational potential of galaxy clusters is reflected in both
their X-ray emission and their imprint on the images of background sources due
to their gravitational lensing effects. Since these projections of the
potential are weighted differently along the line-of-sight, we propose a method
to combine them and remove the degeneracy between two cases: (i) a cluster
consisting of a single potential well, or (ii) an apparent cluster composed of
several potential wells projected onto each other. We demonstrate with
simulated data of potential models that this method indeed allows to
significantly distinguish multiple from single clusters. The confidence limit
for this distinction depends on the mass ratio between the clusters. It ranges
from ~ 15 sigma for mass ratio 1:1 to ~ 4 sigma for mass ratio 1:6.
Furthermore, the method reconstructs the correct cluster mass, the correct mass
ratio of the two clusters, and the correct scale radii with typical fractional
accuracies of a few percent at 3 sigma confidence. As an aside, our method
allows to accurately determine gas fractions in clusters, also with 3 sigma
fractional accuracies of order a few percent. We argue that our method provides
an alternative to the commonly used beta-fit technique, and yields more
reliable results in a broader range of cases.
