# Thread: Rewriting an expression without the absolute value symbols

1. ## Rewriting an expression without the absolute value symbols

$\displaystyle \frac{|x-y|}{|y-x|}$
x cannot equal y.
I'm stumped on this, I'm being told the answer is 1 but I don't understand how.
If someone could explain this indepth I'd be so grateful! Thank you.

2. Originally Posted by tiar
$\displaystyle \frac{|x-y|}{|y-x|}$
x cannot equal y.
I'm stumped on this, I'm being told the answer is 1 but I don't understand how.
If someone could explain this indepth I'd be so grateful! Thank you.
Let $\displaystyle x-y=z$

Then $\displaystyle \frac{|x-y|}{|y-x|} = \frac{|z|}{|-z|} = \frac{|z|}{|z|} = 1$

3. Ohh, I think I get it now. Thank you! I'm very bad with absolute value...
Edit: Wait, I'm still confused. Where does $\displaystyle \frac{|x-y|}{|-x-y|}$ Come from?
(That is, $\displaystyle \frac{|z|}{|-z|}$)

4. Originally Posted by tiar
Ohh, I think I get it now. Thank you! I'm very bad with absolute value...
Edit: Wait, I'm still confused. Where does $\displaystyle \frac{|x-y|}{|-x-y|}$ Come from?
(That is, $\displaystyle \frac{|z|}{|-z|}$)
If z = x - y then

-z = (-1)(x - y) = -x + y = y - x

5. Originally Posted by tiar
Wait, I'm still confused. Where does $\displaystyle \frac{|x-y|}{|-x-y|}$ Come from?
If you do 5 - 3, you get +2.

If you do 3 - 5, you get -2.

If you reverse a subtraction, you kick a "minus" out front.

Have fun!