r=ab/a+b+c
r*(a+b+c)=ab
ra+rb+rc-ab=0
(ra-ab)=-rb-rc
a(r-b)=-r(b+c)
a=-r(b+c)/(r-b)
a=r(b+c)/(b-r)
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Verified answer
r=ab/a+b+c
r*(a+b+c)=ab
ra+rb+rc-ab=0
(ra-ab)=-rb-rc
a(r-b)=-r(b+c)
a=-r(b+c)/(r-b)
a=r(b+c)/(b-r)