Show that x=1-(b/a)satisfies the equation a(a+b)x2-b(a-b)x=(a-b)2,and find the other value of x.

x=(a-b)/a, a(a+b)(a-b)²/a² -(b(a-b)(a-b)/a)=((a-b)/a)=((a-b)/a)(a²-b²+b²-ab)=a(a-b)(a-b)/a =(a-b)²

                other value = (a-b)²/(a(a+b))*(a/(a-b))= (a-b)/(a+b)

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) 

Approved