Find all values of x at which the tangent line to the graph curve is parallel to the line y = x

y = (X^2 + 1)/(X+1)

My Work:

Y' = (2x(x + 1) - (X^2 + 1)) / (X^2 + 2X +1) (Quotient rule)

if y = x, the slope is 1, so Y' = 1

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

X^2 + 2X + 1 = X^2 + 2X - 1

2 = 0

...? What'd I do wrong?