How is this simplified

x-1
------------------
x² - 4 + (x+2)


It's simplified to:

1
------
x+2


how?????

= (x-1)/(x^2+x-4+2)

=(x-1)/(x^2+x-2)

=(x-1)/(x-1)(x+2)

= 1/(x+2)

x^2 - 4 + (x+2) = x^2 + x - 2
x^2 + x - 2 = (x + 2)(x - 1)

Then, (x - 1)/(x + 2)(x - 1) = 1/(x+2)