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how to solve equations like SQRT(x-6)/SQRT(4-x) for their domain

  • algebra -

    The domain will be all real numbers except:
    where the denominator is zero
    one of the radicands is negative

    x-6 >= 0, or x >= 6
    4-x >= 0, or x <= 4
    exclude x=4

    we want all x satisfying all of the above. I don't see any.

    x >= 6 means 4-x < 0
    x < 4 means x-6 < 0

    so, nowhere is there a valid sqrt possible

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