Dear Ritwick,

x=(a-b)/a,

a(a+b)(a-b)²/a² -(b(a-b)(a-b)/a)=(a-b)²

=((a-b)/a)=(a-b)²

=((a-b)/a)(a²-b²+b²-ab)=(a-b)²

=a(a-b)(a-b)/a =(a-b)²

α+β=[-(-b(a-b))]/[a(a+b)]

(a-b)/a +β = [b(a-b)]/[a(a+b)]

β = (a-b)[{b/a(a+b)} - 1/a]

therefore β = (b-a)/(b+a) 

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