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Perform the indicated operation. (2)/(x)+(5)/(3x²)

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Final answer:

To perform the operation (2)/(x) + (5)/(3x²), we find the least common denominator, rewrite the fractions with this denominator, and combine them, obtaining the simplified form (6x + 5)/(3x²).

Step-by-step explanation:

To perform the indicated operation (2)/(x) + (5)/(3x²), we need to find a common denominator and combine the fractions. First, identify the least common denominator (LCD) which in this case is 3x². Rewrite each fraction with the LCD:

  • (2)/(x) becomes (2 · 3x)/(3x²), which simplifies to (6x)/(3x²)
  • (5)/(3x²) already has the denominator 3x²

Combining the fractions we get:

(6x)/(3x²) + (5)/(3x²)

Since we have the same denominator, we can combine the numerators:

(6x + 5)/(3x²)

This is the simplified form of the expression.

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