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x^3-x^2y over x^2-y^2, divided by x^3y over xy^2+y^3

My solution: y over x

Am I right?

  • Algebra -

    again, what about restrictions?

  • Algebra -

    I'm fairly sure that's the extent to which I need to answer these problems.. I'm not looking for x, therefore restrictions are irrelevant

  • Algebra -

    yes they are relevant

    by using the = sign we are saying
    "what I write next will be exactly equal to what I had before"

    (x^2 - 4)/(x-2)
    = (x+2)(x-2)/(x-2)
    = x+2

    for every value of x my last expression x+2 is equal to (x^2 - 4)/(x-2) except when x=2

    when x = 2, our first line is 0/0
    but our last line is 4
    so is 0/0 = 4 ????

    that is why whenever we 'cancel' a variable expression we have to restrict those values that make the divided expression equal to zero.

    that is ....

    (x^2 - 4)/(x-2)
    = (x+2)(x-2)/(x-2)
    = x+2 , x not equal to 2

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