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 ]