Simplifying the expression

X / (X - 1) - ( X - 1)/ (X + 1 )

i canceled the (X-1) and then subtracted and i got an awnser of X-1 / X+1 , is that correct?

(x / (x - 1)) - ((x - 1) / (x + 1))
= ((x(x + 1)) / (x - 1)(x + 1)) - ((x - 1)(x - 1) / (x - 1)(x + 1))
= ((x(x + 1)) - (x - 1)(x - 1)) / ((x - 1)(x + 1))
= (x^2 + x - x^2 + 2x - 1) / (x^2 - 1)
= (3x - 1) / (x^2 - 1)

(X / (X - 1)) - ((X - 1) / (X + 1))

First, set both denominators to be (X - 1)*(X + 1)

X*(X+1) - (X-1)*(X+1) / (X-1)*(X+1)

X - (X - 1) / (X - 1)

1 / (X - 1)