Rearrange (1/x) + (1/y) = 1 for x; answer is y/y-1 = x.

zincmanganese

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The question is to rearrange (1/x) + (1/y) = 1 and the answer is y/y-1 = x.

The working I've got so far is:
1/x = 1/1 - 1/y
Invert the fractions
x = 1 - y

So my question is, how do you get to the right answer? What have I done wrong?
 
The question is to rearrange (1/x) + (1/y) = 1 and the answer is y/y-1 = x.

The working I've got so far is:
1/x = 1/1 - 1/y
Invert the fractions
x = 1 - y

So my question is, how do you get to the right answer? What have I done wrong?

1/1 - 1/y = y/y - 1/y = (y-1)/y

1/x = (y-1)/y

Now we can invert the fractions

x = y/(y-1)
 
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The working I've got so far is:
1/x = 1/1 - 1/y
Invert the fractions
x = 1 - y

This is your mistake. You can't just invert the fractions like that.

Consider this:

\(\displaystyle \frac{1}{3}+\frac{1}{3} = \frac{2}{3}\)

but does

\(\displaystyle \frac{3}{1} +\frac{3}{1} =\frac{3}{2}\) ?? No it doesn't.
 
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