algebraic sleight of hand

Hint: The "answer" can be found on page 223 of "The Man Who Knew Infinity" by Robert Kanigel.


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Quoting from “The Man Who Knew Infinity”, page 223:

“What’s gone wrong? Nothing but that scourge of many an elementary proof: we have divided by zero, a mathematically impermissible operation that gives an ‘answer’ devoid of meaning.

But nowhere, a voice interrupts, does the proof say we should divide by zero.

On the contrary: we started off with a = b, then toward the end divided by a2 – ab, which is zero."

Postscript: The book, "The Man Who Knew Infinity", is the story of an Indian genius, Srinivasa Ramanujan, who didn't fit the expectations of, and was failed by, his family and Indian and British education and scientific culture, despite his genius and remarkable contributions to the field of pure mathematics. This brilliant man died, largely unappreciated, at age 32, ill from tireless work bringing his original and unique contributions to the science of numbers. 

His story is not an unfamiliar one. "The Man Who Knew Infinity" is an excellent book.