To identify the restrictions to the domain of the rational expression:
\[ \frac{1}{x+2} + \frac{5x}{x-4} = \frac{1}{x} \]
we need to determine where the denominators are equal to zero, since division by zero is undefined.
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The first term, \(\frac{1}{x+2}\), has a denominator of \(x + 2\). This expression is undefined when \(x + 2 = 0\) (i.e., \(x = -2\)).
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The second term, \(\frac{5x}{x-4}\), has a denominator of \(x - 4\). This expression is undefined when \(x - 4 = 0\) (i.e., \(x = 4\)).
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The right-hand side, \(\frac{1}{x}\), has a denominator of \(x\). This expression is undefined when \(x = 0\).
Thus, the restrictions on the domain are \(x = -2\), \(x = 0\), and \(x = 4\).
Putting this all together, the restrictions to the domain are:
-2, 0, 4
Given the options you provided, it appears there may be a mistake in the provided answers or their formats. However, the correct restrictions are \(-2, 0, 4\).