To simplify the expression \(\frac{2}{3x} + \frac{5}{2x}\), we first need to find a common denominator. The denominators are \(3x\) and \(2x\). The least common denominator (LCD) is \(6x\).
Next, we need to rewrite each fraction with the common denominator:
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For \(\frac{2}{3x}\): \[ \frac{2}{3x} = \frac{2 \cdot 2}{3x \cdot 2} = \frac{4}{6x} \]
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For \(\frac{5}{2x}\): \[ \frac{5}{2x} = \frac{5 \cdot 3}{2x \cdot 3} = \frac{15}{6x} \]
Now we add the two fractions: \[ \frac{4}{6x} + \frac{15}{6x} = \frac{4 + 15}{6x} = \frac{19}{6x} \]
Thus, the simplified expression is: \[ \frac{19}{6x} \]
So the correct answer is: E. \(\frac{19}{6x}\)
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