Solve `(x)/(x+2) le (1)/(|x|)`

Explanation

To solve the inequality \(\frac{x}{x+2} \leq \frac{1}{|x|}\), we will proceed step by step.

### Step 1: Understand the inequality
The inequality involves a fraction on both sides. The right side, \(\frac{1}{|x|}\), is defined for \(x \neq 0\) since the absolute value cannot be zero.

### Step 2: Multiply both sides by \(|x|\)
Since \(|x|\) is always positive (except at \(x = 0\), which we will exclude), we can multiply both sides by \(|x|\) without changing the direction of the inequality:
\[
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