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Simplify. Express your answer as a single fraction in simplest form. $\newline$ $\frac{7r}{3} + \frac{1}{7s}$

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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{7r}{3} + \frac{1}{7s}

Identify LCM: Identify the least common multiple (LCM) of the denominators $3$ and $7s$ . Since $3$ and $7s$ have no common factors other than $1$ , the LCM is simply their product, which is $21s$ .
Convert fractions: Convert each fraction to have the LCM as the denominator. To do this, multiply the numerator and denominator of the first fraction by $7s$ to get $(7r \times 7s) / (3 \times 7s)$ and multiply the numerator and denominator of the second fraction by $3$ to get $(1 \times 3) / (7s \times 3)$ .
Perform multiplications: Perform the multiplications from Step $2$ . This gives us $(49rs) / (21s)$ for the first fraction and $3 / (21s)$ for the second fraction.
Add fractions: Add the two fractions together. Since they now have the same denominator, we can add the numerators directly. This gives us $(49rs + 3) / (21s)$ .
Check for simplification: Check if the expression can be simplified further. In this case, the numerator and the denominator have no common factors other than $1$ , so the expression is already in its simplest form.

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