Andrews' q-Dyson conjecture asserts that the constant term of a certain Laurent polynomial is a product of simple factors. It was proposed by Andrews in 1975 and proved by Zeilberger and Bressoud in 1985. We give the second proof of the theorem by using partial fractions and iterated Laurent series. The underlying idea is that two polynomials of degree n agreeing at n+1 points are identical. This is a joint work with Ira Gessel.