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(1 / A) + (1 / B) = 1 / 12
(1 / A) + [1 / (A - 7)] = 1 / 12
12 A - 84 + 12 A = A * (A - 7)
24 A - 84 = A² - 7 A
0 = A² - 31 A + 84
factor the quadratic to find A