We study D-s(+) decays to final states involving the eta' with a 482 pb(-1) data sample collected at root s = 4.009 GeV with the BESIII detector at the BEPCII collider. We measure the branching fractions B(D-s(+) -> eta'X) = (8.8 +/- 1.8 +/- 0.5)% and B(D-s(+) > eta'rho(+)) = (5.8 +/- 1.4 +/- 0.4)% where the first uncertainty is statistical and the second is systematic. In addition, we estimate an upper limit on the non-resonant branching ratio B(D-s(+) -> eta'pi(+)pi(0)) < 5.1% at the 90% confidence level. Our results are consistent with CLEO's recent measurements and help to resolve the disagreement between the theoretical prediction and CLEO's previous measurement of B(D-s(+) -> eta'rho(+)). (C) 2015 The Authors. Published by Elsevier B.V.