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

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

\newline

Answer:

Identify LCD: Identify the least common denominator (LCD) for the two fractions. $\newline$ The LCD for the fractions $(\frac{1}{2x^{3}})$ and $(\frac{1}{3})$ is $6x^{3}$ because $6x^{3}$ is the smallest number that both denominators $(2x^{3}$ and $3)$ will divide into evenly.
Rewrite fractions: Rewrite each fraction with the LCD as the new denominator. $\newline$ For the first fraction, $(1)/(2x^{3})$ , we multiply the numerator and denominator by $3$ to get $(3)/(6x^{3})$ . $\newline$ For the second fraction, $(1)/(3)$ , we multiply the numerator and denominator by $2x^{3}$ to get $(2x^{3})/(6x^{3})$ .
Perform subtraction: Perform the subtraction of the two fractions. $\newline$ Now that both fractions have the same denominator, we can subtract their numerators: $\newline$ $(\frac{3}{6x^{3}}) - (\frac{2x^{3}}{6x^{3}}) = \frac{3 - 2x^{3}}{6x^{3}}$
Simplify fraction: Simplify the resulting fraction if possible. $\newline$ The fraction $(3 - 2x^{3})/(6x^{3})$ 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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