If (−2x)/((5 − x)(3 − x)) ≡ 5/(5 − x) + A/(3 − x), what is A?

Correct answer: b −3

Putting x = 3: −6 = A(5 − 3) = 2A, so A = −3.

Why the other options are wrong

• a −5: Putting x = 3: −6 = A(5 − 3) = 2A; with A = −5 we would get −10, but −6 is needed.
• c 3: With A = 3, 2A = 6, but −6 is needed; the sign is negative.
• d 5: 5 is the numerator of the first part, not A; A = −3.