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What is the process to list all numbers for which rational expression is undefined? Ex: y-3divided y+5

  • math -

    Look to see if the expression contains any fractions.
    Those fractions cannot be zero, since we cannot divide by zero.
    So take each of the fractions and set them equal to zero and solve.
    You now have the value of the variable that we cannot use.

    in your example,
    (y-3)/(y+5)

    y+5 = 0
    y = -5

    so:
    (y-3)/(y+5), y ≠ -5

    in some cases the could be more than one restriction.
    e.g. 5x/(x^2 - x - 6)

    x^2 - x - 6 = 0
    (x-3)(x+2) = 0
    x= 3 or x = -2

    So we have :
    5x/(x^2 - x - 6) , x ≠-2, 3

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