The theory of framed motives by Garkusha and Panin gives computations in the stable motivic homotopy category SH(k) in terms of Voevodsky's framed correspondences. In particular, the motivically fibrant Ω-resolution in positive degrees of the motivic suspension spectrum ΣP1∞X+, where X+=X⨿⁎, for a smooth scheme X∈Smk over an infinite perfect field k, is computed. The computation by Garkusha, Neshitov and Panin of the framed motives of relative motivic spheres (Al×X)/((Al−0)×X), X∈Smk, is one of ingredients in the theory. In the article we extend this result to the case of a pair (X,U) given by a smooth affine variety X over k and an open subscheme U⊂X. The result gives an explicit motivically fibrant Ω-resolution in positive degrees for the motivic suspension spectrum ΣP1∞(X+/U+) of the quotient-sheaf X+/U+.