SOLUTION: 1/a+1/b=c solve for b i don't know how to get the variables on one side

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Question 48458: 1/a+1/b=c
solve for b
i don't know how to get the variables on one side
Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
+%281%2Fa%29%2B%281%2Fb%29=c+
+1%2Fb+=+c-%281%2Fa%29+

And now to get b, we just invert both sides:
+b+=+1%2F%28c-%281%2Fa%29%29+

which is not a particular "tidy" answer, so what mathematicians tend to do is this:

from +1%2Fb+=+c-%281%2Fa%29+ we re-write the right hand side:
+1%2Fb+=+%28%28ac%29%2Fa%29-%281%2Fa%29+
+1%2Fb+=+%28ac-1%29%2Fa+

and then we invert:
+b+=+a%2F%28ac-1%29+

which is tidier since we don't need the "1/" bit anymore, we just flip the fraction straight away.

I hope this is clear?

jon.