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Simplify. Express your answer as a single fraction in simplest form. $\newline$ $\frac{2}{xy} + \frac{y}{3}$

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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}{xy} + \frac{y}{3}

Find LCM of Denominators: Find the least common multiple (LCM) of the denominators $xy$ and $3$ . Since $xy$ and $3$ have no common factors other than $1$ , the LCM is simply $xy \times 3$ , which is $3xy$ .
Make Denominators Same: Make the denominators the same by multiplying the first fraction by $3$ and the second fraction by $xy$ . This gives us $(\frac{2}{xy}) \cdot (\frac{3}{3}) + (\frac{y}{3}) \cdot (\frac{xy}{xy})$ , which simplifies to $(\frac{6}{3xy}) + (\frac{y^2}{3xy})$ .
Add Numerators: Now that the denominators are the same, we can add the numerators. The new numerator will be $6 + y^2$ , and the denominator remains $3xy$ . So the combined fraction is $\frac{6 + y^2}{3xy}$ .
Check for Simplification: Check if the fraction can be simplified further. Since $6$ and $y^2$ have no common factors, and the denominator $3xy$ does not have any common factors with the numerator, the fraction is already in its simplest form.

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