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Simplify. Express your answer as a single fraction in simplest form. $\newline$ $\frac{1}{2} + \frac{q^4}{3}$

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Add and subtract rational expressions

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Q. Simplify. Express your answer as a single fraction in simplest form.

\newline

\frac{1}{2} + \frac{q^4}{3}

Identify Fractions: Identify the fractions to be added. $\newline$ We have two fractions: $\frac{1}{2}$ and $\frac{q^4}{3}$ . To add them, we need a common denominator.
Find LCD: Find the least common denominator (LCD) for the fractions. $\newline$ The denominators are $2$ and $3$ . The LCD for $2$ and $3$ is $6$ because it is the smallest number that both $2$ and $3$ can divide into without a remainder.
Convert to LCD: Convert each fraction to an equivalent fraction with the LCD as the denominator. $\newline$ For $\frac{1}{2}$ , we multiply the numerator and the denominator by $3$ to get $\left(\frac{1\times 3}{2\times 3}\right) = \frac{3}{6}$ . $\newline$ For $\frac{q^4}{3}$ , we multiply the numerator and the denominator by $2$ to get $\left(\frac{q^4\times 2}{3\times 2}\right) = \frac{2q^4}{6}$ .
Add Fractions: Add the fractions with the common denominator. $\newline$ Now we add the numerators while keeping the denominator the same: $(\frac{3}{6}) + (\frac{2q^4}{6}) = \frac{3 + 2q^4}{6}$ .
Simplify Expression: Simplify the expression if possible. $\newline$ The expression $(3 + 2q^4)/6$ is already in its simplest form because the numerator and the denominator have no common factors other than $1$ .

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