isolating the letter C =b(1/c-1/d)

Question

A= b(1/c-1/d)

Answer 1

A= b(1/c-1/d)

 

A/b = 1/c - 1/d

 

A/b + 1/d = 1/c

 

1 / ( A/b + 1/d ) = c

 

or c = bd / (Ad + b)

Answer 2

A = b (1/c -1/d)

 

A = b/c - b/d

 

A + b/d = b/c                      (multiply A by d/d or by an appropriate form of 1)

 

(ad + b)/d = b/c 

 

d/(ad + b) = c/b                   (invert both fractions or cross multiply twice)

 

bd/(ad +b) = c                        (multiply both sides by b to get c alone on the right and you're done)  

Answer 3

A = b[(1/c) -(1/d)] = (b/c) + (b/d)

 

Multiply both sides by c

 

Ac = b + (bc/d)

 

 Multiply both sides by (d/b)

 

[(Acd)/b] = d + c

 

[(Acd)/b] - c = d

 

c[Ad/(b- 1)] = d

 

c = [d(b - 1)]/Ad