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Simplify. Express your answer as a single fraction in simplest form. \newline2rs−r3s53\frac{2}{rs} - \frac{r^3s^5}{3}

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Full solution

Q. Simplify. Express your answer as a single fraction in simplest form. \newline2rs−r3s53\frac{2}{rs} - \frac{r^3s^5}{3}
  1. Find Common Denominator: Identify the common denominator for the fractions.\newlineSince the fractions have different denominators, we need to find a common denominator to combine them. The denominators are rsrs and 33. The least common denominator (LCD) is 3rs3rs.
  2. Rewrite Fractions: Rewrite each fraction with the common denominator.\newlineWe will multiply the numerator and denominator of the first fraction by 33 to get the common denominator of 3rs3rs.\newline2rs×33=63rs\frac{2}{rs} \times \frac{3}{3} = \frac{6}{3rs}\newlineFor the second fraction, we will multiply the numerator and denominator by 11, as it already has the common denominator.\newliner3s53×11=r3s53rs\frac{r^3s^5}{3} \times \frac{1}{1} = \frac{r^3s^5}{3rs}
  3. Combine Fractions: Combine the fractions.\newlineNow that both fractions have the common denominator of 3rs3rs, we can combine them.\newline(6−r3s5)/3rs(6 - r^3s^5) / 3rs
  4. Simplify Expression: Simplify the expression if possible.\newlineIn this case, there are no like terms in the numerator, and the expression is already in its simplest form.\newlineFinal expression: (6−r3s5)/3rs(6 - r^3s^5) / 3rs

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