Assume:
\(\displaystyle \dfrac {a}{b} \ = \ \dfrac {c}{d} \) →
\(\displaystyle \dfrac {a}{b} + 1 \ = \ \dfrac {c}{d} + 1 \) →
\(\displaystyle \dfrac {a+b}{b} \ = \ \dfrac {c+d}{d} \) ......................................(1) →
Then
\(\displaystyle \dfrac {a}{b} \ = \ \dfrac {c}{d} \) →
\(\displaystyle \dfrac {a}{b} - 1 \ = \ \dfrac {c}{d} - 1 \) →
\(\displaystyle \dfrac {a - b}{b} \ = \ \dfrac {c - d}{d} \) ......................................(2)
Divide (1) by (2) to get
\(\displaystyle \dfrac {a+b}{a - b} \ = \ \dfrac {c + d}{c - d} \) ........................(3)
apply (3) into the given equation to get the desired result