jmc

The expression is only undefined when the denominator is equal to zero. Therefore, the goal is to find the product of all real $x$ that satisfy the equation $x^2+2x-3=0$. Since the discriminant of this quadratic is $2^2-4(1)(-3)=16$, which is positive, we know that the roots of $x^2+2x-3$ are distinct real numbers. The product of the roots of a quadratic of the form of $a{x}^2+bx+c$ is equal to $\frac{c}{a}$, so the desired product of the values of $x$ for which $x^2+2x-3=0$ is $\frac{-3}{1}$, or $\boxed{-3}$.