1/(a+b) = c/a + d/b
a/(a+b) = c + d*a/b
a= bc + ad ... (1)
a+b = b ...(2)
b or c equals 0
I hope c = 0 ... and don't know that.
The above formula doesn't succeed.
Because 1/2 = 2/4
But, it looks interesting.
At least,
1/(a+b) = C*(c/a + d/b)