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Simplify. Express your answer as a single fraction in simplest form. $\newline$ $\frac{3}{v} + 8v$

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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{3}{v} + 8v

Identify Common Denominator: Identify the common denominator for the two terms in the expression. Since one term is a fraction with a denominator of $v$ and the other term is a whole number, we can rewrite the whole number with a denominator of $v$ to combine them into a single fraction.
Rewrite Whole Number as Fraction: Rewrite the whole number $8v$ as a fraction with a denominator of $v$ . To do this, we multiply $8v$ by $\frac{v}{v}$ (which is equal to $1$ ) to get the equivalent fraction $\frac{8v^2}{v}$ .
Combine Fractions: Combine the two fractions over the common denominator. $\newline$ Now we have the two fractions $\frac{3}{v}$ and $\frac{8v^2}{v}$ , which can be combined because they have the same denominator. $\newline$ $(\frac{3}{v}) + (\frac{8v^2}{v}) = \frac{3 + 8v^2}{v}$
Check for Simplification: Check for any simplification. $\newline$ The numerator $3 + 8v^2$ cannot be simplified further because there are no common factors between the terms. The denominator $v$ is already in its simplest form.
Write Final Answer: Write the final answer. $\newline$ The expression $\frac{3}{v} + 8v$ simplifies to $\frac{3 + 8v^2}{v}$ .

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