so, we forcus on the bold below formula.
1/(a+b) = c/a + d/b
c*b/a*b + a*d/a*b = ( c*b + a*d ) / a*b
c*b + a*d = C
a+b=C*a*b
a + b = (c*b + a*d)*a* b
the above looks also interesting.
abc = 1 ...(1)
abd = 1 ...(2)
we could replace,
bc = 1/a
bd = 1/a