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Revisiting precalculus just for fun.
Enjoy.
Enjoy.
b/(ax-1)-a/(bx-1)=0.........common denominator is(ax-1)(bx-1)
b(bx-1)/((ax-1)(bx-1))-a(ax-1)/((ax-1)(bx-1))=0...........both sides multiply by (ax-1)(bx-1)
b(bx-1)-a(ax-1)=0
b^2*x-b-(a^2*x-a)=0
b^2*x-b-a^2*x+a=0
b^2*x-a^2*x=b-a
(b^2-a^2)x=b-a
x=(b-a)/(b^2-a^2)...........factor b^2-a^2=(b-a)(b+a)
x=(b-a)/((b-a)(b+a))........simplify
x=1/(b+a) where View attachment 2533 and View attachment 2535