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Thread: rational expressions. help plz!

  1. #1
    Junior Member
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    rational expressions. help plz!

    When mutiplying this...

    x - 5x + 4 X x + 2x - 3
    x + 3x - 28 x + 10x +21

    ...is to factor out?

    But, what do i do if i can't find out factors?? Because im not sure how to factor them
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  2. #2
    Senior Member topher0805's Avatar
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    Left Side:

    $\displaystyle \frac {x^2 - 5x + 4}{x^2 + 3x - 28}$

    Use the sum and product method.

    The top equates to:

    $\displaystyle (x-4)(x-1)$

    And the bottom equates to:

    $\displaystyle (x+7)(x-4)$

    The $\displaystyle (x-4)$ terms cancel out so the left side of your expression is:

    $\displaystyle \frac {x-1}{x+7}$

    Right Side:

    $\displaystyle \frac {x^2 + 2x - 3}{x^2 + 10x +21}$

    The top equates to:

    $\displaystyle (x+3)(x-1)$

    The bottom equates to:

    $\displaystyle (x+3)(x+7)$

    The $\displaystyle (x+3)$ terms cancel out, so your right side expression is:

    $\displaystyle \frac {x-1}{x+7}$

    Rules of fractions say that we simply multiply the top by the top, and the bottom by the bottom to get:

    $\displaystyle
    \frac {(x-1)^2}{(x+7)^2}$
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