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

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

\newline

Answer:

Find Common Denominator: To add the fractions $(5)/(2x^{3})$ and $(3)/(5)$ , we need to find a common denominator. The denominators are currently $2x^3$ and $5$ . The least common denominator (LCD) is the product of the distinct prime factors of each denominator, which in this case is $2x^3 \times 5$ .
Express Fractions: Now we need to express each fraction with the common denominator of $10x^3$ . To do this, we multiply the numerator and denominator of each fraction by the factor needed to reach the common denominator. For the first fraction, $\frac{5}{2x^{3}}$ , we multiply by $\frac{5}{5}$ to get $\frac{25}{10x^{3}}$ . For the second fraction, $\frac{3}{5}$ , we multiply by $\frac{2x^3}{2x^3}$ to get $\frac{6x^3}{10x^{3}}$ .
Add Fractions: Next, we add the two fractions with the common denominator: $(\frac{25}{10x^{3}}) + (\frac{6x^3}{10x^{3}})$ . This gives us a single fraction: $(\frac{25 + 6x^3}{10x^{3}})$ .
Simplify Final Answer: The fraction $(25 + 6x^3)/(10x^{3})$ is already in simplest form because the numerator and denominator have no common factors other than $1$ . Therefore, this is our final answer.

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