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Simplify. Express your answer as a single fraction in simplest form. $\newline$ $\frac{x}{3} + \frac{5}{wx^3}$

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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{x}{3} + \frac{5}{wx^3}

Identify common denominator: Identify the common denominator. $\newline$ To add the fractions $\frac{x}{3}$ and $\frac{5}{wx^3}$ , we need to find a common denominator. The least common denominator (LCD) for $3$ and $wx^3$ is $3wx^3$ .
Rewrite with common denominator: Rewrite each fraction with the common denominator. $\newline$ We need to adjust each fraction so that they both have the common denominator of $3wx^3$ . $\newline$ For the first fraction, $\frac{x}{3}$ , we multiply the numerator and denominator by $wx^3$ to get $\frac{x \cdot wx^3}{3 \cdot wx^3}$ . $\newline$ For the second fraction, $\frac{5}{wx^3}$ , we multiply the numerator and denominator by $3$ to get $\frac{5 \cdot 3}{wx^3 \cdot 3}$ .
Perform multiplications: Perform the multiplications. $\newline$ Now we perform the multiplications from Step $2$ . $\newline$ For the first fraction, $(x \cdot wx^3) / (3 \cdot wx^3)$ simplifies to $(wx^4) / (3wx^3)$ . $\newline$ For the second fraction, $(5 \cdot 3) / (wx^3 \cdot 3)$ simplifies to $15 / (3wx^3)$ .
Combine fractions: Combine the fractions. $\newline$ Now that both fractions have the common denominator, we can combine them. $\newline$ $(wx^4) / (3wx^3) + 15 / (3wx^3) = (wx^4 + 15) / (3wx^3)$
Simplify numerator: Simplify the numerator. $\newline$ We can't simplify $wx^4 + 15$ any further, so the numerator remains as is. $\newline$ $\frac{wx^4 + 15}{3wx^3}$
Simplify fraction: Simplify the fraction. $\newline$ We look for any common factors in the numerator and denominator that can be canceled out. In this case, there are no common factors to cancel. $\newline$ $(wx^4 + 15) / (3wx^3)$ is already in simplest form.

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