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Math Help - Simplify Rational Expression

  1. #1
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    Simplify Rational Expression

    simplify each rational expression. find all numbers that must be excluded from the domain of the simplified rational expression.

    y^2 + 7y - 18 / y^2 - 3y + 2

    got it down to

    y + 9 / y - 1

    y cannot equal 1

    the answer in the book says y cannot equal 1 or 2. why the 2?
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  2. #2
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    Re: Simplify Rational Expression

    Quote Originally Posted by PaperStSoap View Post
    simplify each rational expression. find all numbers that must be excluded from the domain of the simplified rational expression.

    y^2 + 7y - 18 / y^2 - 3y + 2

    got it down to

    y + 9 / y - 1

    y cannot equal 1

    the answer in the book says y cannot equal 1 or 2. why the 2?
    Assuming that your expression is \displaystyle \begin{align*} \frac{y^2 + 7y - 18}{y^2 - 3y + 2} \end{align*} (please use brackets where they're needed, or else learn some LaTeX), then we have

    \displaystyle \begin{align*} \frac{y^2 + 7y - 18}{y^2 - 3y + 2} &\equiv \frac{(y + 9)(y - 2)}{(y - 1)(y -2)}\textrm{ with }y \neq \{1, 2\} \textrm{ since the denominator can not be 0} \\ &\equiv \frac{y + 9}{y - 1} \textrm{ with } y \neq \{ 1, 2\} \end{align*}

    Basically you need to take into account all restrictions implied by the ORIGINAL definition of your function.
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  3. #3
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    Re: Simplify Rational Expression

    got it. thanks for the prompt answer.
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