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Math Help - factoring rational expression

  1. #1
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    factoring rational expression

    Hello, I want to factor the following:
    1-(1/y^2)

    I thought that this would be the correct answer:
    1/y * (y-(1/y))

    however my textbook says that this is correct:
    (1-1/y) (1+1/y)

    Can someone please tell me if my answer is just another way of how they did it in the second example, or am I wrong ?

    Thanks
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  2. #2
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    Re: factoring rational expression

    Quote Originally Posted by fran1942 View Post
    Hello, I want to factor the following:
    1-(1/y^2)

    I thought that this would be the correct answer:
    1/y * (y-(1/y))

    however my textbook says that this is correct:
    (1-1/y) (1+1/y)

    Can someone please tell me if my answer is just another way of how they did it in the second example, or am I wrong ?

    Thanks
    \displaystyle \begin{align*} 1 - \frac{1}{y^2} &= 1^2 - \left(\frac{1}{y}\right)^2 \\ &= \left(1 - \frac{1}{y}\right)\left(1 + \frac{1}{y}\right) \end{align*}

    by the Difference of Two Squares rule...
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  3. #3
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    Re: factoring rational expression

    thanks kindly, but can you tell me how I am wrong with this answer:

    1/y * (y-(1/y))

    Thanks.
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  4. #4
    Super Member Quacky's Avatar
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    Re: factoring rational expression

    You're not wrong, it's just that rather than simplifying by removing common factors, you've made the expression more complicated.

    I could write 3x+5 as  \frac{x^2}{94}(\frac{282}{x}+\frac{470}{x^2}) if I wanted to, but would you class that as splitting it into its factors?
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