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

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Simplify mixed rational expressions

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Q. Simplify. Express your answer as a single fraction in simplest form.

\newline

\frac{3}{2p^5} + 9q

Identify Common Denominator: Identify the common denominator for the fractions. $\newline$ Since the first term is already a fraction, we need to express the second term, $9q$ , as a fraction with the same denominator as the first term to be able to combine them. The common denominator will be $2p^5$ .
Convert Integer to Fraction: Convert the integer term to a fraction with the common denominator. $\newline$ To convert $9q$ to a fraction with the denominator $2p^5$ , we multiply both the numerator and the denominator by $2p^5$ . $\newline$ $9q \times (\frac{2p^5}{2p^5}) = \frac{18p^5q}{2p^5}$
Combine Fractions: Combine the fractions over the common denominator. $\newline$ Now we can add the two fractions since they have the same denominator. $\newline$ $(\frac{3}{2p^5}) + (\frac{18p^5q}{2p^5}) = \frac{3 + 18p^5q}{2p^5}$
Simplify Numerator: Simplify the numerator if possible. $\newline$ In this case, the numerator cannot be simplified further because $3$ and $18p^5q$ do not have any common factors. $\newline$ So the final simplified expression is $(3 + 18p^5q)/(2p^5)$

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