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Simplify. Express your answer as a single fraction in simplest form. \newliner4+3rs\frac{r}{4} + \frac{3}{rs}

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Full solution

Q. Simplify. Express your answer as a single fraction in simplest form. \newliner4+3rs\frac{r}{4} + \frac{3}{rs}
  1. Identify LCD: r4+3rs\frac{r}{4} + \frac{3}{rs}\newlineIdentify the least common denominator (LCD) for the fractions.\newlineThe LCD for 44 and ss is 4s4s.
  2. Rewrite fractions: r4+3rs\frac{r}{4} + \frac{3}{rs}\newlineRewrite each fraction with the common denominator 4s4s.\newliner⋅s4⋅s+3⋅4r⋅4s\frac{r \cdot s}{4 \cdot s} + \frac{3 \cdot 4}{r \cdot 4s}\newline=rs4s+124rs=\frac{rs}{4s} + \frac{12}{4rs}
  3. Combine fractions: (rs4s)+(124rs)(\frac{rs}{4s}) + (\frac{12}{4rs})\newlineCombine the fractions over the common denominator.\newline(rs+124rs)(\frac{rs + 12}{4rs})
  4. Check for simplification: (rs+12)/(4rs)(rs + 12)/(4rs)\newlineCheck if the numerator and denominator have common factors that can be simplified. In this case, there are no common factors to simplify.

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