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Simplify. Express your answer as a single fraction in simplest form. $\newline$ $\frac{1}{9q} + \frac{r}{3}$

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Add and subtract rational expressions

Full solution

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

\newline

\frac{1}{9q} + \frac{r}{3}

Rewrite with common denominator: Rewrite both fractions with the common denominator $9q$ . $\newline$ $\frac{1}{9q}$ is already with the correct denominator, so it remains the same. $\newline$ For $\frac{r}{3}$ , multiply both the numerator and the denominator by $3q$ to get the same denominator as $\frac{1}{9q}$ . $\newline$ $\frac{r}{3} \times \frac{3q}{3q} = \frac{3qr}{9q}$
Combine fractions: Combine the two fractions with the common denominator. $(1 + 3qr)/9q$
Check for simplification: Check if the numerator can be simplified further. Since $1$ and $3qr$ do not have common factors, the numerator is already in its simplest form.
Write final answer: Write the final answer as a single fraction in simplest form. The final answer is $(1 + 3qr)/9q$ .

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