The way you have written it, without parentheses, it simplifies to

x + (1/1) - x = 1

If you intend parentheses, it doesn't really simplify. It can be divided out into a whole number and a fraction.

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

Some of us like to see the leading denominator variable have a positive sign. Then you would have

(-x-1)/(x-1)

x + (1/1) - x = 1

If you intend parentheses, it doesn't really simplify. It can be divided out into a whole number and a fraction.

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

Some of us like to see the leading denominator variable have a positive sign. Then you would have

(-x-1)/(x-1)