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Math Help - Simplifying Rational Expressions HELP

  1. #1
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    Simplifying Rational Expressions HELP

    Hi all,

    I cannot understand why this does not work.


    \frac{x^{2} + 6x + 5}{x^{2} -x -2}


    So I thought I could just cancel out the fraction x^2 in both the numerator and dominator as it is a common factor.
    Why does this not work?


    For example, the fraction below we can simplify it by dividing top and bottom by 5 and p^2 as they are common factors.

    \frac{60p^{3}q}{35p^{5}r} = \frac{12q}{7p^{2}r}

    So why does the above one not let us divide by x^2 as it is also a common factor?
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  2. #2
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    Re: Simplifying Rational Expressions HELP

    Hint :

    x^2+6x+5=(x+1)(x+5)
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  3. #3
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    Re: Simplifying Rational Expressions HELP

    That doesn't explain anything to me :S

    I know what a quadradric is but I still don't get why we can't factor out the top and bottom by x^2.
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  4. #4
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    Re: Simplifying Rational Expressions HELP

    The problem is that you have an incorrect idea of what a factor is! x^2 is NOT a factor in both numerator and denominator because it is added, not multiplied. "Factors" are parts of products, not sums.
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  5. #5
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    Re: Simplifying Rational Expressions HELP

    \frac{4+5}{4+2}\neq \frac{5}{2}
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