  We introduce the notion of balanced pair of additive subcategories in an
abelian category. We give sufficient conditions under which the balanced pair
of subcategories gives rise to equivalent homotopy categories of complexes. As
an application, we prove that for a left-Gorenstein ring, there exists a
triangle-equivalence between the homotopy category of its Gorenstein projective
modules and the homotopy category of its Gorenstein injective modules, which
restricts to a triangle-equivalence between the homotopy category of projective
modules and the homotopy category of injective modules. In the case of
commutative Gorenstein rings we prove that up to a natural isomorphism our
equivalence extends Iyengar-Krause's equivalence.
