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Math Help - Is there any difference between -2/(2x-3) and -(2/(2x-3))?

  1. #1
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    Is there any difference between -2/(2x-3) and -(2/(2x-3))?

    Hi,

    as stated above, is there any difference between -2/(2x-3) and -(2/(2x-3))?

    Thanks
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  2. #2
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    Re: Is there any difference between -2/(2x-3) and -(2/(2x-3))?

    Hey FailInMaths.

    There is no difference between the two expressions.
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  3. #3
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    Re: Is there any difference between -2/(2x-3) and -(2/(2x-3))?

    Hello, FailInMaths!

    \text{Is there any difference between }\,\frac{-2}{2x-3}\,\text{ and }\;-\frac{2}{2x-3}\,?

    As chiro pointed out, there is no difference.


    Here is a baby-talk explanation.

    Consider the fraction \frac{\text{-}3}{4}
    Since "negative divided by positive is negative": . \frac{\text{-}3}{4} \:=\:\text{-}\frac{3}{4}

    Consider the fraction \frac{3}{\text{-}4}
    Since "positive divided by negative is negative": . \frac{3}{\text{-}4} \:=\:\text{-}\frac{3}{4}

    So we have: . \frac{\text{-}3}{4} \;=\;\frac{3}{\text{-}4} \;=\;\text{-}\frac{3}{4}


    My high school math teacher explained it like this:

    A fraction has three signs: . \pm\frac{\pm a}{\pm b}
    . . the sign of the numerator, the sign of the denominator, and the sign of the fraction.

    We can change any two of the signs without changing the value.


    For example: . \frac{-3}{4} is actually {\color{green}+}\frac{{\color{green}-}3}{{\color{green}+}4}

    Change any two signs: . {\color{green}+} \frac{{\color{red}+}3}{{\color{red}-}4}\;=\;{\color{red}-}\frac{{\color{green}-}3}{{\color{red}-}4} \;=\;{\color{red}-}\frac{{\color{red}+}3}{{\color{green}+}4}

    See?
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  4. #4
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    Re: Is there any difference between -2/(2x-3) and -(2/(2x-3))?

    That's a good explanation reminds me of when I was back in 8th grade taking Algebra I.
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  5. #5
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    Re: Is there any difference between -2/(2x-3) and -(2/(2x-3))?

    Ic, thank you for the detailed explanation =)
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