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Math Help - quick question with simplifying rational expressions

  1. #1
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    quick question with simplifying rational expressions

    I just need some confirmation to whether or not these are right,

    can I simplify  -\frac{3x^2}{2x} into  \frac{3x}{2} ?

    can \frac{x+3}{x+6} be simplified to  \frac1{2} ?
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  2. #2
    Member Jonboy's Avatar
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    on the first you're correct. and let me tell you why.

    you have: \frac{ - 3x^2}{2x}

    Pull out the x on top and bottom: \frac{ x(-3x)}{x(2)}

    this is the same as: \frac{x}{x}\cdot \frac{-3x}{2}

    \frac{x}{x} is one. anything divided by itself is one (except zero).

    So you're left with: 1\cdot\frac{-3x}{2} = \frac{-3x}{2}

    But there's another way to think about this, a more easier way.

    you can just cancel the x's: \frac{ \not x(-3x)}{\not x(2)}

    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~


    On the second problem, you're wrong.

    There's nothing you can factor out on the top and bottom.

    but say you had: \frac{4x + 8}{2x + 6}

    now you can pull out factors: \frac{2(2x + 4)}{2(x + 3)} = \frac{ \not 2 (2x + 4)}{ \not 2 (x + 3)}

     = \frac{2x + 4}{x + 3}
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  3. #3
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    Thank you
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