Categories
Math Puzzles Variable Substitutions

Mathematical Quickies No.226

So for some reason I never started looking for substitutions when solving equations. It was certainly something I learned to do when analyzing circuits, but when I see a math problem I never started looking for substitutions that might simplify the problem. Until recently.

Looking at, I think this problem, it “just clicked” – and I started looking for substitutions. Then used them to nock out answers for the next half dozen puzzle problems I tackled. Weird, since I am not doing anything I did not know before, but I just started looking at problems differently.

This one is fairly straight forward:

Solve: (x-a)/b + (x-b)/a = b/(x-a) + a/(x-b)

It becomes way easier to solve after a simple substitution.
My Solution.

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