I'm stumped at how to solve the following for a: 1/r=1/a+1/b

It looks like a parallel reistance formula. I've seen it written like that or r=1/(1/a+1/b); usually written as 1/Rt=1/R1+1/R2+1+1/R3... +1/Rn

Start by deducting 1/b from both sides. Then take the reciprocal of both sides (which you can do because every number--other than zero--has exactly one multiplicative inverse; so if x = y then it's also true that 1/x = 1/y.)

You'll immediately arrive at an equation of the form KISS described, except it'll be solved for a instead of r.