SOLUTION: if 1/a = 1/b - 1/c ,what is the value of c

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Question 1124733: if 1/a = 1/b - 1/c ,what is the value of c
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
The denominators are a, b and c. The lowest common denominator LCD is the product of all three values: a*b*c

If we multiply everything by the LCD, then the denominators cancel out making the fractions go away.

1%2Fa+=+1%2Fb+-+1%2Fc

a%2Ab%2Ac%2A%281%2Fa%29+=+a%2Ab%2Ac%2A%281%2Fb%29+-+a%2Ab%2Ac%2A%281%2Fc%29 Multiply each of the three terms by the LCD a*b*c

Notice these pairs match up

Those same pairs divide and cancel out (since x/x = 1 where x is nonzero)

b%2Ac+=+a%2Ac+-+a%2Ab The fractions are gone at this point. Let's isolate c

b%2Ac+-+a%2Ac++=+-a%2Ab Subtract ac from both sides

c%28b+-+a%29++=+-a%2Ab Factor out the common factor c

c++=+%28-a%2Ab%29%2F%28b+-+a%29 Divide both sides by (b-a)

The answer is c++=+%28-a%2Ab%29%2F%28b+-+a%29