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Simplify. Express your answer as a single fraction in simplest form. $\newline$ $\frac{c^5}{2} - \frac{d}{3}$

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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{c^5}{2} - \frac{d}{3}

Identify LCD: Identify the least common denominator (LCD) for the fractions. $\newline$ The denominators are $2$ and $3$ , so the LCD is $2 \times 3 = 6$ .
Rewrite fractions: Rewrite each fraction with the common denominator of $6$ . For the first fraction, multiply both the numerator and the denominator by $3$ to get $\frac{3c^5}{6}$ . For the second fraction, multiply both the numerator and the denominator by $2$ to get $\frac{2d}{6}$ .
Combine fractions: Combine the fractions over the common denominator. $\newline$ $(\frac{3c^5}{6} - \frac{2d}{6} = \frac{3c^5 - 2d}{6})$
Check for simplification: Check if the numerator can be simplified further. $\newline$ The terms in the numerator, $3c^5$ and $2d$ , do not have common factors other than $1$ , so the numerator cannot be simplified further.

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