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There are two options open for you.
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One is, these are simultaneous equations.
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You've got to find a way to solve for x and t
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in terms of x' and t' and
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all these funny functions involving u.
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You treat them all as constants and juggle them around,
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multiply by this, divide by that,
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but you shouldn't do that
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because you know what the answer should be.
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The answer should be
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the same as what I got with the velocity reversed.
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So, x should be x'+u·t' over the square root.