The numerator $x^{2}-4$ is a difference of squares, which can be factored as $(x-2)(x+2)$. The denominator $x^{2}+2x$ can be factored by taking out a common factor of $x$, which gives us $x(x+2)$.
So, the expression becomes:
$$\frac{x^{2}-4}{x^{2}+2 x} =
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