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Simplify. Express your answer as a single fraction in simplest form. $\newline$ $\frac{rs^2}{3} - \frac{3}{s}$

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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{rs^2}{3} - \frac{3}{s}

Identify common denominator: $\frac{rs^2}{3} - \frac{3}{s}$ $\newline$ Identify the common denominator, which in this case is $3s$ .
Rewrite with common denominator: $\frac{rs^2}{3} - \frac{3}{s}$ $\newline$ Rewrite both terms with the common denominator $3s$ . $\newline$ $\left(\frac{rs^2 \cdot s}{3 \cdot s}\right) - \left(\frac{3 \cdot 3}{s \cdot 3}\right)$
Simplify numerators: $(rs^2 \cdot s)/(3 \cdot s) - (3 \cdot 3)/(s \cdot 3)$ $\newline$ Simplify the numerators. $\newline$ $(rs^3)/(3s) - (9)/(3s)$
Combine fractions: $(\frac{rs^3}{3s}) - (\frac{9}{3s})$ $\newline$ Combine the fractions. $\newline$ $(\frac{rs^3 - 9}{3s})$
Check for common factors: $\frac{rs^3 - 9}{3s}$ $\newline$ Check if the numerator and denominator have any common factors that can be simplified. In this case, there are no common factors, so the fraction is already in simplest form.

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