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Simplify. Express your answer as a single fraction in simplest form. \newliner2+rs3\frac{r}{2} + \frac{rs}{3}

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Full solution

Q. Simplify. Express your answer as a single fraction in simplest form. \newliner2+rs3\frac{r}{2} + \frac{rs}{3}
  1. Identify common denominator: Identify the common denominator for the fractions r2\frac{r}{2} and rs3\frac{rs}{3}. The common denominator for 22 and 33 is 66. We will rewrite both fractions with the common denominator of 66.
  2. Rewrite fractions: Rewrite each fraction with the common denominator.\newliner2\frac{r}{2} can be written as r×32×3=3r6\frac{r \times 3}{2 \times 3} = \frac{3r}{6}.\newliners3\frac{rs}{3} can be written as rs×23×2=2rs6\frac{rs \times 2}{3 \times 2} = \frac{2rs}{6}.
  3. Add fractions: Add the two fractions with the common denominator.\newline(\frac{\(3\)r}{\(6\)}) + (\frac{\(2\)rs}{\(6\)}) = (\frac{\(3\)r + \(2\)rs}{\(6\)})\.
  4. Simplify numerator: Simplify the numerator if possible.\(\newlineIn this case, the numerator 3r+2rs3r + 2rs cannot be simplified further because there are no common factors that can be factored out.
  5. Write final answer: Write the final answer.\newlineThe simplified expression is (3r+2rs)/6(3r + 2rs)/6.

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