Keep in mind, because they didn't give us any values we can only find what a equals in terms of the other variables. You'll see what I mean after we get to the final answer.
r = (ab)/(a+b)
Multiply both sides by (a+b)
r(a+b) = (ab)
Divide by r on both sides.
(a+b) = (ab)/r
Subtract b on both sides.
a = ((ab)/r) - b
You can't simplify it any further to my knowledge. Well, besides getting a common denominator with b and subtracting them, but it won't really simplify things.
Now. Let's get a better answer... haha. Here we go:
r = (ab)/(a+b)
Same step. Multiply on both sides.
r(a+b) = (ab)
This time distribute the r to all values.
ar + br = (ab)
Subtract ar on both sides.
ar + br - ar = ab - ar
br = ab - ar
Next step! Factor "a" out of ab - ar by making it a quantity time "a" with "a" removed... it's easier to show than to explain. So here you go:
