Question

Solve the following:
1) x-a/x+b = a+b/a-b

Answer 1

x-a/x+b=a+b/a-b

using componendo and dividendo

(x-a+x+b)/(x-a-x-b)=(a+b+a-b)/(a+b-a+b)

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

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

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

2x={b(a-b)-a(a+b)}/b

2x={ab-b^2-a^2-ab}/b

x=-(a^2+b^2)/2b