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.

Please help.

Herk

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KnifeMissile

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:
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)...

aberkok

OF COURSE the answer ends up coming from Waterloo, Ontario....

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Herk

Yeah, I feel kind of silly after actually sitting down and putting some effort into it. I reallized I had thought way to much about it.

1/a + 1/b = 1

ab(1/a) + ab(1/b) = ab

b + a = ab

b/a + a/a = ab/a

b/a + 1 = b

b/a = b - 1

b = a(b - 1)

a = b/(b - 1)

Although, I admit that you solution was much easier and more intuitive. Thank you kindly for your insight.

Herk

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-Blind faith runs into things!-