Solve For x...5

Revisiting precalculus just for fun.
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

 

Don't you just love precalculus? Do you miss the course?