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Simplify. Express your answer as a single fraction in simplest form. $\newline$ $\frac{5}{3v w^{4}}$ $+$ $2$

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Simplify mixed rational expressions

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

\newline

\frac{5}{3v w^{4}}

+

2

Identify common denominator: Identify the common denominator for the fractions. $\newline$ Since $2$ is a whole number, we can express it as a fraction with the same denominator as the first term to combine them. The first term has a denominator of $3vw^4$ , so we will use that for the whole number as well.
Convert whole number to fraction: Convert the whole number $2$ into a fraction with the common denominator. $\newline$ To convert $2$ into a fraction with the denominator $3vw^4$ , we multiply both the numerator and the denominator of $\frac{2}{1}$ by $3vw^4$ . $\newline$ $\frac{2 \times (3vw^4)}{1 \times 3vw^4} = \frac{6vw^4}{3vw^4}$
Combine fractions: Combine the fractions. $\newline$ Now that both terms have the same denominator, we can add the numerators together. $\newline$ $(\frac{5}{3vw^4}) + (\frac{6vw^4}{3vw^4}) = \frac{5 + 6vw^4}{3vw^4}$
Simplify fraction: Simplify the fraction. $\newline$ The fraction $(5 + 6vw^4)/(3vw^4)$ is already in simplest form because the numerator and the denominator do not have any common factors other than $1$ .

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