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solve for a if 1/a + 1/b = 1/c
1/a + 1/b = 1/c
Subtract 1/b from both sides
1 /a = 1/c - 1 / b get a common denominator on the right
1 / a = [ b - c ] / bc and we can write
a / 1 = bc / [ b - c ]
a = bc / [ b - c ]