y² - 1
———————
 1 - y

First let's arrange the denominator 

 1 - y

in descending order:

-y + 1

Foctor out -1

-1(y - 1)


Now we have 

  y² - 1
—————————
-1(y - 1)

Factor the numerator, the difference of two squares 

(y - 1)(y + 1)
——————————————
-1(y - 1)

Now when we remove the factor of 1, also called "cancelling
the y-1's", we get:

(y + 1)
———————
  -1

or

-(y + 1)

or

-y - 1

Edwin