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

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

Identify LCM: Identify the least common multiple (LCM) of the denominators $9q$ and $p$ . Since $9q$ and $p$ have no common factors other than $1$ , the LCM is simply their product, $9qp$ .
Rewrite fractions: Rewrite each fraction with the common denominator of $9qp$ . To do this, multiply the numerator and denominator of the first fraction by $p$ , and the numerator and denominator of the second fraction by $9q$ . This gives us $(5p)/(9qp) + (18q)/(9qp)$ .
Combine fractions: Combine the fractions by adding their numerators together, since they now have the same denominator. The combined fraction is $(5p + 18q)/(9qp)$ .
Check for simplification: Check if the numerator can be simplified or if there are any common factors between the numerator and the denominator. In this case, there are no common factors between $(5p + 18q)$ and $9qp$ , so the fraction is already in its simplest form.

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