Hi,
as stated above, is there any difference between -2/(2x-3) and -(2/(2x-3))?
Thanks
Hello, FailInMaths!
$\displaystyle \text{Is there any difference between }\,\frac{-2}{2x-3}\,\text{ and }\;-\frac{2}{2x-3}\,?$
As chiro pointed out, there is no difference.
Here is a baby-talk explanation.
Consider the fraction $\displaystyle \frac{\text{-}3}{4}$
Since "negative divided by positive is negative": .$\displaystyle \frac{\text{-}3}{4} \:=\:\text{-}\frac{3}{4}$
Consider the fraction $\displaystyle \frac{3}{\text{-}4}$
Since "positive divided by negative is negative": .$\displaystyle \frac{3}{\text{-}4} \:=\:\text{-}\frac{3}{4}$
So we have: .$\displaystyle \frac{\text{-}3}{4} \;=\;\frac{3}{\text{-}4} \;=\;\text{-}\frac{3}{4}$
My high school math teacher explained it like this:
A fraction has three signs: .$\displaystyle \pm\frac{\pm a}{\pm b}$
. . 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: .$\displaystyle \frac{-3}{4}$ is actually $\displaystyle {\color{green}+}\frac{{\color{green}-}3}{{\color{green}+}4}$
Change any two signs: .$\displaystyle {\color{green}+} \frac{{\color{red}+}3}{{\color{red}-}4}\;=\;{\color{red}-}\frac{{\color{green}-}3}{{\color{red}-}4} \;=\;{\color{red}-}\frac{{\color{red}+}3}{{\color{green}+}4}$
See?