- #1

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## Homework Statement

Simplify: x^2 - y^2 - 4y - 4 / x^2 - y^2 -4x + 4

The answer (according to the back of the book) should be: x + y + 2 / x + y - 2

## Homework Equations

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## The Attempt at a Solution

I've tried multiple combinations to try to get the correct answer. Here is my closest one:

x^2 - y^2 - 4y - 4 / x^2 - y^2 - 4x + 4 =

Using the difference of the squares and distributive property to factor I got:

(x + y)(x - y) -4(y +1) / (x + y)(x-y) -4(x-1) =

Simplify by getting rid of like terms:

(y + 1) / (x - 1)

I'm pretty sure I'm missing some combination between GCF, factoring, Perfect Square Trinomials, and/or Difference of Squares. I just can't see which ones to use that will give me the right answer.