ab=(a+b)^2/(a^2-b^2)=(a+b)/(a-b) Note that if a=3 and b=4: 3*4=12≠(3+4)/(3-4), because 12≠-7.
ab(a-b)-a-b=0; a^2b-ab^2-a=b; a^2-a(b^2+1)/b=1
Complete the square: a^2-a(b^2+1)/b+(b^2+1)^2/(4b^2)=1+(b^2+1)^2/(4b^2)
(a-(b^2+1)/(2b))^2=1+(b^2+1)^2/(4b^2)
a-(b^2+1)/(2b)=√(1+(b^2+1)^2/(4b^2)) so we can relate a and b.
One solution is b=1, a=1+√2.