How does this simplification happen?

Question

I can't seem to figure out the math that takes the left equation and turns it into what's in the middle and right.

Answer 1

x²/(x+1) - (x-1)

To add them, they must be over a common denominator, which is (x+1). So multiply (x-1) by (x+1)/(x+1):

x²/(x+1) - (x-1)(x+1)/(x+1)

x²/(x+1) - (x²-1)/(x+1)

(x² - x² + 1)/(x+1) = 1/(x+1)