Solve For x...4

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Revisiting precalculus just for fun.
Enjoy.

IMG_20220409_181547.jpg
 
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
upload_2022-4-9_17-57-50.gif
and
upload_2022-4-9_17-58-37.gif
 

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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

A nice walk through precalculus just for fun.
 

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