\(x * y = x + y - xy\)Let \(x^{-1}\) be the inverse of x, so that\(x * x^{-1} = x + x^{-1} - x(x^{-1}) = 0\)\(x + x^{-1} - x(x^{-1}) = 0 \implies x(x^{-1}) - x^{-1} = x\)\(x^{-1}(x - 1) = x \implies x^{-1} = \frac{x}{x - 1}\)= \(\frac{x}{-(1 - x)} = \frac{-x}{1 - x}, x \neq 1\)

A binary operation * is defined on the set of real numbers, R, by \(x * y = x + y - xy\). If the identity element under the operation * is 0, find the inverse of \(x \in R\).

Earlier discussion