Make B the subject of the relation : 1/a is equal to 1/b + c

By making ‘a’ the subject, I believe you mean isolate the variable ‘a’.

1/a - 1/b = 1/c : add 1/b to both sides

1/a = 1/b + 1/c : combine the unlike fractions by finding a common denominator, bc is the common denominator

1/a = (1/b)(c/c) + (1/c)(b/b) : simplify

1/a = (c/bc) + (b/bc) : add numerators only, because the denominators match

1/a = (c + b)/bc : multiply both sides by a

1 = (a)[(c + b)/bc] : multiply both sides by the reciprocal of [(c + b)/bc] which is [bc/(b + c)]

1[bc/(b + c)] = a

a = bc/(b + c)

This will not work if c = -b, because then you would be dividing by zero.

Example: 1/2 - 1/3 = 1/6 a = 2, b = 3 c= 6

a = bc/(b + c) => 2 = (3 x 6)/(3 + 6) => 2 = 18/9 => 2 = 2.

Step-by-step explanation: