Solve For x...4

Revisiting precalculus just for fun.
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 and

 

A nice walk through precalculus just for fun.