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

**FailInMaths** · December 27th 2012, 11:04 PM

Hi,

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

Thanks

**chiro** · December 28th 2012, 12:37 AM

Hey FailInMaths.

There is no difference between the two expressions.

**Soroban** · December 28th 2012, 05:32 AM

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?

**SMAD** · December 28th 2012, 05:41 AM

That's a good explanation reminds me of when I was back in 8th grade taking Algebra I.

**FailInMaths** · December 28th 2012, 06:53 AM

Ic, thank you for the detailed explanation =)

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