# Simplify Rational Expression

• Jan 19th 2009, 03:09 PM
autumnafternoon
Simplify Rational Expression
(y-1)²-x²

I did this but I'm not sure it's correct:

-1(x²-(y-1)²) =

(y-1)²-x²

-x²+(y-1)² =
(y-1)²-x²

(y-1)²-x² = 1????
(y-1)²-x²

Thank you!

• Jan 19th 2009, 03:19 PM
Jester
Quote:

Originally Posted by autumnafternoon
(y-1)²-x²

I did this but I'm not sure it's correct:

-1(x²-(y-1)²) = why this and not $\displaystyle -\left( (y-1)^2 - x^2 \right)$
(y-1)²-x²

-x²+(y-1)² =
(y-1)²-x²

(y-1)²-x² = 1????
(y-1)²-x²

Thank you!

Very close! See above.
• Jan 19th 2009, 03:29 PM
autumnafternoon
I'm sorry....I don't understand. Is the answer the same but my process wrong?
• Jan 19th 2009, 03:52 PM
Jester
Quote:

Originally Posted by autumnafternoon
I'm sorry....I don't understand. Is the answer the same but my process wrong?

No, what I'm saying is that the numerator

$\displaystyle x^2 - (y-1)^2 = -\left( (y-1)^2 - x^2 \right)$

so

$\displaystyle \frac{x^2 - (y-1)^2}{(y-1)^2-x^2 } = \frac{-\left( (y-1)^2 - x^2 \right)}{(y-1)^2-x^2 } = -1$
• Jan 19th 2009, 04:19 PM
autumnafternoon
Omg! You wouldn't believe how many times I had to repeat that process until what you wrote sunk in....doh! (Doh). Thank you SO much for your help!