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Simplify. Express your answer as a single fraction in simplest form. \newline9p5+25pq\frac{9p}{5} + \frac{2}{5pq}

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Q. Simplify. Express your answer as a single fraction in simplest form. \newline9p5+25pq\frac{9p}{5} + \frac{2}{5pq}
  1. Identify Common Denominator: Identify the common denominator for the fractions 9p5\frac{9p}{5} and 25pq\frac{2}{5pq}. Since both denominators already contain the number 55, and the second denominator has an additional variable qq, the common denominator is 5pq5pq.
  2. Rewrite Fractions: Rewrite each fraction with the common denominator. The first fraction, 9p5\frac{9p}{5}, needs to be multiplied by qq\frac{q}{q} to have the common denominator, becoming 9pq5pq\frac{9pq}{5pq}. The second fraction, 25pq\frac{2}{5pq}, already has the common denominator, so it remains unchanged.
  3. Add Fractions: Add the two fractions now that they have a common denominator. This gives us (9pq+2)/5pq(9pq + 2)/5pq.
  4. Check Numerator Simplification: Check if the numerator can be simplified. In this case, 9pq9pq and 22 do not have any common factors other than 11, so the numerator cannot be simplified further.
  5. Check Fraction Simplification: Check if the fraction itself can be simplified. Since pp and qq are variables and we do not know their values, we cannot simplify the fraction further without additional information. Therefore, the final answer is (9pq+2)/5pq(9pq + 2)/5pq.

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