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Revisiting precalculus just for fun.
Enjoy.
Enjoy.
1-(a/b)(1-a/x)-(b/a)(1-b/x)=0
1-(a/b)((x-a)/x)-(b/a)((x-b)/x)=0
1-(a(x-a))/(bx)-(b(x-b))/(ax)=0..........common denominator is abx, multiply both sides
abx-a^2(x-a)-b^2(x-b)=0
abx-a^2*x+a^3-b^2*x+b^3=0
abx-a^2*x-b^2*x=-a^3-b^3....isolate x
x(ab-a^2-b^2)=-(a^3+b^3)
x=-(a^3+b^3)/(ab-a^2-b^2).........(ab-a^2-b^2)=-(a^2-ab+b^2)
x=-(a^3+b^3)/-(a^2-ab+b^2)............cancel minuses and factor a^3+b^3=(a + b) (a^2 - a b + b^2)
x=((a + b) (a^2 - a b + b^2))/(a^2-ab+b^2)......simplify
x=a + b