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Math Help - [SOLVED] Simplification of Algebraic fractions

  1. #1
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    [SOLVED] Simplification of Algebraic fractions

    Q. Simplify:

    \frac {(a + b)^2 - c^2} {3a + 3b - 3c}

    i've got up to

    \frac {a^2 + 2ab +b^2 - c^2} {3(a + b - c)}

    but i can't simplify it further unless \frac {a^2 + 2ab +b^2 - c^2} {3(a + b - c)} is replaced by \frac {a^2 + b^2 - c^2}{3(a + b - c)} then i could work my way to the answer, but im not sure if that should be the right method
    because of the rule, (a + b)^2 = a^2 + 2ab + b^2

    btw the answer is \frac {a + b - c}3
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  2. #2
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    Quote Originally Posted by waven View Post
    Q. Simplify:

    \frac {(a + b)^2 - c^2} {3a + 3b - 3c}

    i've got up to

    \frac {a^2 + 2ab +b^2 - c^2} {3(a + b - c)}

    but i can't simplify it further unless \frac {a^2 + 2ab +b^2 - c^2} {3(a + b - c)} is replaced by \frac {a^2 + b^2 - c^2}{3(a + b - c)} then i could work my way to the answer, but im not sure if that should be the right method
    because of the rule, (a + b)^2 = a^2 + 2ab + b^2

    btw the answer is \frac {a + b - c}3
    Note the numerator is the difference of squares


    \frac {(a + b)^2 - c^2} {3a + 3b - 3c}=\frac{(a+b-c)(a+b+c)}{3(a+b-c)}=\frac{a+b+c}{3}
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