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For (px + q)/((x − a)(x − b)) with distinct roots, the cover-up rule gives A = (pa + q)/(a − b) and B = (pb + q)/(b − a). As a consistency check A + B must equal p, the coefficient of x.
Cover-up rule
A = (pa + q)/(a − b), B = (pb + q)/(b − a)
A = (3 + 5)/3 = 8/3 and B = (−6 + 5)/(−3) = 1/3, and 8/3 + 1/3 = 3 = p as required.
A repeated factor (x − a)² needs terms A/(x − a) + B/(x − a)², which this two-distinct-root form does not cover.