Ooooh, I finally found your question in the quoted calculations.
If you have then you can simplify
Apply similar transformations with all summands in the numerator and you'll get the next line of my calculations.
And now the 2nd question:
All my calculations were necessary to get a rational denominator. Thus I multiplied numerator and denominator by which I marked in red. That means I didn't change the value of the quotient.
The product of the numerator and is
which I simplified to