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Math Help - Simplify fraction.

  1. #1
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    Simplify fraction.

    a^2 - 2ab + b^2 / a - b
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  2. #2
    Super Member wingless's Avatar
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    Please use parentheses. I assume you wanted to say (a^2 - 2ab + b^2) / (a-b)

    \frac{a^2 - 2ab + b^2}{a-b}

    Do you know that a^2 - 2ab + b^2 = (a-b)^2 ?
    If you didn't know, you learned now

    \frac{(a-b)^2}{a-b}

    \frac{(a-b)(a-b)}{(a-b)}

    \boxed{~a-b~}
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  3. #3
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    Quote Originally Posted by wingless View Post
    Please use parentheses. I assume you wanted to say (a^2 - 2ab + b^2) / (a-b)

    \frac{a^2 - 2ab + b^2}{a-b}

    Do you know that a^2 - 2ab + b^2 = (a-b)^2 ?
    If you didn't know, you learned now

    \frac{(a-b)^2}{a-b}

    \frac{(a-b)(a-b)}{(a-b)}

    \boxed{~a-b~}
    Hey, thanks. I never knew that.

    Now what would it be if the denominator was a + b?
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  4. #4
    Super Member wingless's Avatar
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    Quote Originally Posted by elliotfsl View Post
    Hey, thanks. I never knew that.

    Now what would it be if the denominator was a + b?
    \frac{a^2 - 2ab + b^2}{a+b}

    Well, there's nothing much to do with this fraction.. Start with adding and subtracting 4ab,

    \frac{a^2 - 2ab + b^2 + 4ab - 4ab}{a + b}

    \frac{a^2 + 2ab + b^2 - 4ab}{a + b}

    \frac{(a+b)^2 - 4ab}{a + b}

    \frac{(a+b)^2}{a + b} - \frac{4ab}{a + b}

    a + b - \frac{4ab}{a + b}
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