# Math Help - Simplify Rational Expression

1. ## 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!

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

3. I'm sorry....I don't understand. Is the answer the same but my process wrong?

4. 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

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

so

$\frac{x^2 - (y-1)^2}{(y-1)^2-x^2 } = \frac{-\left( (y-1)^2 - x^2 \right)}{(y-1)^2-x^2 } = -1$

5. Omg! You wouldn't believe how many times I had to repeat that process until what you wrote sunk in....doh! . Thank you SO much for your help!