Your equations are right. Let's use a+b=a/b. Rewrite as: ab+b^2=a, so b^2+ab=a, so a(1-b)=b^2. For a to be positive b must be between 0 and 1 or 0<b<1. a^2-b^2=(a-b)(a+b)=a+b, because the difference of the squares is equal to a+b. So dividing both sides by a+b we get a-b=1, so a=1+b. Therefore substituting for a in a(1-b)=b^2 we get 1-b^2=b^2, and 2b^2=1, from which b=sqrt(1/2) or sqrt(2)/2 and a=1+sqrt(2)/2. Therefore approximately b=0.7071 and a=1.7071. The smaller number is 0.7071.