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Originally Posted by Herk
How do you solve this for a?
1/a + 1/b = 1
I was able to come to a = (a+b)/b, but where to go from there? Is that it? Surely not.
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I suspect your first mistake was trying to "cross-multiply," which didn't lead you anywhere interesting.
The correct method of isolation will be so simple that you'll wonder why you didn't see it, yourself. Try doing this:
Code:
1/a + 1/b = 1
1/a = 1 - 1/b (isolate the term with the wanted variable)
a = 1/(1 - 1/b) (reciprocate both sides)
So, this is the formula for
a, with three provisions.
The first two should be obvious. Neither
a nor
b may be zero, since division by zero is undefined.
The third provision may come as a surprise but
(1 - 1/b) may not be zero, either, since we divide by it. In other words,
b ≠ 1. You can even see that this must be so because, in the original equation, if
b were one, then the reciprocal of
a must be zero, which is pretty hard to do (mild understatement)...