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Simplify. Express your answer as a single fraction in simplest form. $\newline$ $\frac{2}{rs} - \frac{r^3s^5}{3}$

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Add and subtract rational expressions

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

\newline

\frac{2}{rs} - \frac{r^3s^5}{3}

Find Common Denominator: Identify the common denominator for the fractions. $\newline$ Since the fractions have different denominators, we need to find a common denominator to combine them. The denominators are $rs$ and $3$ . The least common denominator (LCD) is $3rs$ .
Rewrite Fractions: Rewrite each fraction with the common denominator. $\newline$ We will multiply the numerator and denominator of the first fraction by $3$ to get the common denominator of $3rs$ . $\newline$ $\frac{2}{rs} \times \frac{3}{3} = \frac{6}{3rs}$ $\newline$ For the second fraction, we will multiply the numerator and denominator by $1$ , as it already has the common denominator. $\newline$ $\frac{r^3s^5}{3} \times \frac{1}{1} = \frac{r^3s^5}{3rs}$
Combine Fractions: Combine the fractions. $\newline$ Now that both fractions have the common denominator of $3rs$ , we can combine them. $\newline$ $(6 - r^3s^5) / 3rs$
Simplify Expression: Simplify the expression if possible. $\newline$ In this case, there are no like terms in the numerator, and the expression is already in its simplest form. $\newline$ Final expression: $(6 - r^3s^5) / 3rs$

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