  We give a new method for the evaluation of a class of integrals of rational
symmetric functions in N pairs of variables {x_a, y_a}_{a=1,... N} arising in
coupled matrix models, valid for a broad class of two-variable measures. The
result is expressed as the determinant of a matrix whose entries consist of the
associated biorthogonal polynomials, their Hilbert transforms, evaluated at the
zeros and poles of the integrand, and bilinear expressions in these. The method
is elementary and direct, using only standard determinantal identities, partial
fraction expansions and the property of biorthogonality. The corresponding
result for one-matrix models and integrals of rational symmetric functions in N
variables {x_a}_{a=1,... N} is also rederived in a simple way using this method
