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Math Help - Comparing Two Quantities

  1. #1
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    Comparing Two Quantities

    I have two quantities, A and B. I need to know which is larger or whether they are equivalent.

    Quantity A: X^2 + 2xy +y^2/x + y
    Quantity B: x + y + 2

    Note: X + Y does not equal zero.

    Thank you!
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  2. #2
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    Quote Originally Posted by wizkid94 View Post
    I have two quantities, A and B. I need to know which is larger or whether they are equivalent.

    Quantity A: X^2 + 2xy +y^2/x + y
    Quantity B: x + y + 2

    Note: X + Y does not equal zero.

    Thank you!
    if this is what you meant by quantity A ...

    \dfrac{x^2+2xy+y^2}{x+y}

    ... factor the numerator and simplify, then compare.
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  3. #3
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    I factored and I have x^2 + 2y for A, compared against x + y + 2 for B. My book says that quantity B is bigger. Why is this?

    OK I think I might have made a mistake in factoring. In quantity, A, should x^2 still have the denominator of x + y? If this is so, by plugging in numbers, quantity does indeed prove to be bigger. So, I guess my question is when you cross out the x + y of the numerator after factoring, does the x^2 retain its denominator of x + y or does it also go?
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  4. #4
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    is what "skeeter" wrote to you true ? is that what you meant by quantity A ?
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  5. #5
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    Yes.
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  6. #6
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    Quote Originally Posted by wizkid94 View Post
    Yes.
    You needed BRACKETS then: (x^2 + 2xy +y^2) / (x + y) ; OK?

    HINT: (x + y)(x + y) = ?
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  7. #7
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    Quote Originally Posted by Wilmer View Post
    You needed BRACKETS then: (x^2 + 2xy +y^2) / (x + y) ; OK?

    HINT: (x + y)(x + y) = ?
    That would equal the numerator, leaving us with x-y for Quantity A, and still x + y + 2 for B. But still, then, how do we know which quantity is larger? All we know is that x + y does not equal 0. Say X were 3 and y were -8. Quantity A would be larger.
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  8. #8
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    Quote Originally Posted by wizkid94 View Post
    That would equal the numerator, leaving us with x-y for Quantity A,...
    No: leaves Quantity A = x + y ; don't "rush" so much !
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  9. #9
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    Quote Originally Posted by Wilmer View Post
    No: leaves Quantity A = x + y ; don't "rush" so much !
    Thank you, thank you. I have been doing math for 6 hours today so my brain is fried.
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