  We use the tridiagonal representation approach to solve the radial
Schr\"odinger equation for an inverse power-law potential of a combined quartic
and sextic degrees and for all angular momenta. The amplitude of the quartic
singularity is larger than that of the sextic but the signs are negative and
positive, respectively. It turns out that the system has a finite number of
bound states, which is determined by the larger ratio of the two singularity
amplitudes. The solution is written as a finite series of square integrable
functions written in terms of the Bessel polynomial.
