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

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

\newline

Answer:

Find Common Denominator: To add the two fractions, we need to find a common denominator. The least common denominator (LCD) for $5x^3$ and $2$ is $10x^3$ .
Rewrite Fractions: Rewrite each fraction with the common denominator of $10x^3$ .
$(1)/(5x^{3})$ becomes $(2)/(10x^{3})$ because we multiply both the numerator and the denominator by $2$ .
$(1)/(2)$ becomes $(5x^3)/(10x^3)$ because we multiply both the numerator and the denominator by $5x^3$ .
Add Fractions: Now that both fractions have the same denominator, we can add them together. $\newline$ $(\frac{2}{10x^{3}}) + (\frac{5x^3}{10x^3}) = \frac{2 + 5x^3}{10x^3}$
Simplify Numerator: Simplify the numerator by combining like terms. $2 + 5x^3$ does not have like terms, so it remains as is. The simplified fraction is $(2 + 5x^3)/(10x^3)$ .
Check for Further Simplification: Check to see if the fraction can be simplified further. Since there are no common factors between the numerator and the denominator, the fraction is already in its simplest form.

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