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$Perform the operation and express your answer as a single fraction in simplest form. (5)/(x^(3))+(1)/(2) Answer:$

Perform the operation and express your answer as a single fraction in simplest form. $\newline$ $\frac{5}{x^{3}}+\frac{1}{2}$ $\newline$ Answer:

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Roots of rational numbers

Full solution

Q. Perform the operation and express your answer as a single fraction in simplest form.

\newline

\frac{5}{x^{3}}+\frac{1}{2}

\newline

Answer:

Find Common Denominator: To add the two fractions $(5)/(x^{3})$ and $(1)/(2)$ , we need to find a common denominator. The least common denominator (LCD) for $x^3$ and $2$ is $2x^3$ .
Rewrite Fractions: Rewrite each fraction with the common denominator $2x^3$ . The first fraction $\frac{5}{x^{3}}$ is already over $x^3$ , so we just need to multiply the numerator and denominator by $2$ to get $\frac{10}{2x^{3}}$ . The second fraction $\frac{1}{2}$ needs to be multiplied by $\frac{x^3}{x^3}$ to get $\frac{x^3}{2x^{3}}$ .
Add Fractions: Now that both fractions have the common denominator, we can add them together. So we have $(\frac{10}{2x^{3}}) + (\frac{x^3}{2x^{3}})$ .
Combine Numerators: Add the numerators together while keeping the common denominator the same. This gives us $(10 + x^3)/(2x^{3})$ .
Simplify Fraction: The fraction $(10 + x^3)/(2x^{3})$ is already in its simplest form because the numerator and the denominator do not have any common factors other than $1$ .

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