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I have an equation that I've been given the task to solve as part of a course I am doing:

x = (y * a - z * b) / (u * (b - a))

This has worked fine, but in the only question I have left, b - a = 0, in which case u * (b - a) = 0 and therefore I am trying to divide by 0.

I am literally tearing my hair out trying to solve this - how do I rearrange it so that I can calculate x when b - a = 0?

Btw, I am happy to state that this is unsolvable in these circumstances, but I must be certain that it is before I submit my work.

Martin
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2 Answers2

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Whenever people write $x/y$, there's almost always an implicit assumption that $y \neq 0$. In your example, $x$ is undefined when $b-a=0$; it simply does not make sense to ask what the value of the function would be there.

Joe
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  • I've rearranged an equation to end up with the one giving me the problem. I think I'll post a new question with the equation I've rearranged to see if someone can advise what I may have done incorrectly. There is definitely an answe to the question I am told, so perhaps the issue is with my work – Martin Jan 12 '21 at 20:57
  • @Martin Okay, good luck with solving your problem. Make sure to post all of the necessary details needed for people to help you. – Joe Jan 12 '21 at 21:03
  • @Martin, in that case you'll have to tackle the case $a = b$ separately (before rearranging). – vonbrand Jan 14 '21 at 16:20
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x = (y * a - z * b) / (u * (b - a))

comes from something like $$u(b-a)x=ya-zb$$ if $b-a=0$ that is if $b=a$ the LHS becomes $0$ $$0=(y-z)b$$ Now we have two possibilities:

  1. if RHS is zero,e.g. if $y=z$, the equation is indeterminate and has infinite solutions
  2. if RHS is not zero the equation is impossible and there is no solution.

Hope this helps

Raffaele
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