Verified Answer :

\(a = b ( \frac{1}{c}- \frac{1}{d}) \\ a = \frac{b}{c}- \frac{b}{d} \\ \frac{b}{c}=a+ \frac{b}{d} \\ \frac{b}{c}= \frac{ad+b}{d} \\ c = b : \frac{ad+b}{d} \\ c = \frac{bd}{ad+b}\)