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Simplify. Express your answer as a single fraction in simplest form. \newline32p5+9q\frac{3}{2p^5} + 9q

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Simplify mixed rational expressionsright chevron icon

Full solution

Q. Simplify. Express your answer as a single fraction in simplest form. \newline32p5+9q\frac{3}{2p^5} + 9q
  1. Identify Common Denominator: Identify the common denominator for the fractions.\newlineSince the first term is already a fraction, we need to express the second term, 9q9q, as a fraction with the same denominator as the first term to be able to combine them. The common denominator will be 2p52p^5.
  2. Convert Integer to Fraction: Convert the integer term to a fraction with the common denominator.\newlineTo convert 9q9q to a fraction with the denominator 2p52p^5, we multiply both the numerator and the denominator by 2p52p^5.\newline9q×(2p52p5)=18p5q2p59q \times (\frac{2p^5}{2p^5}) = \frac{18p^5q}{2p^5}
  3. Combine Fractions: Combine the fractions over the common denominator.\newlineNow we can add the two fractions since they have the same denominator.\newline(32p5)+(18p5q2p5)=3+18p5q2p5(\frac{3}{2p^5}) + (\frac{18p^5q}{2p^5}) = \frac{3 + 18p^5q}{2p^5}
  4. Simplify Numerator: Simplify the numerator if possible.\newlineIn this case, the numerator cannot be simplified further because 33 and 18p5q18p^5q do not have any common factors.\newlineSo the final simplified expression is (3+18p5q)/(2p5)(3 + 18p^5q)/(2p^5)

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