Polynomials and fractions

Assuming \(x\neq 0\), \(x\neq \pm 1\), \(y\neq 0\), simplify the expression. \[ \left [\left ( \frac{x} {x + 1}\right )^{2} : \left (\frac{x - 1} {y} \right )^{2}\right ] : \frac{2xy} {x^{2} - 1} \]

Assuming \(x\neq \pm y\) and \(y\neq 2x\), simplify the expression: \[ \left ( \frac{2x} {x + y} + \frac{y} {x - y} - \frac{y^{2}} {x^{2} - y^{2}}\right ) : \left ( \frac{1} {x + y} + \frac{x} {x^{2} - y^{2}}\right ) \]

Assuming \(x\neq 0\) and \(y\neq 0\), simplify the following expression. \[ \left (\frac{x^{-2}y^{2}} {x^{0}y^{-8}}\right )^{-2} : \frac{x^{2}} {x^{-4}y^{7}} \]

Find the domain of the following expression. \[ \frac{x^{2} - x} {x + 1} : \frac{x^{2} - 1} {x^{2} + 2x + 1} \]