Resources

Resources

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

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

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

Full solution

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

\newline

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

\newline

Answer:

Identify LCD: Identify the least common denominator (LCD) for the fractions. $\newline$ The LCD for the fractions $(\frac{1}{2x})$ and $(\frac{5}{3x^{3}})$ is $6x^3$ because $6$ is the least common multiple of $2$ and $3$ , and $x^3$ is the highest power of $x$ that appears in the denominators.
Rewrite fractions: Rewrite each fraction with the LCD as the new denominator. $\newline$ For the first fraction $(1)/(2x)$ , multiply the numerator and denominator by $3x^2$ to get $(3x^2)/(6x^3)$ . $\newline$ For the second fraction $(5)/(3x^{3})$ , multiply the numerator and denominator by $2$ to get $(10)/(6x^3)$ .
Combine over LCD: Combine the fractions over the common denominator. $\newline$ Now that both fractions have the same denominator, we can combine them: $\newline$ $(3x^2)/(6x^3) - (10)/(6x^3) = (3x^2 - 10)/(6x^3)$
Simplify numerator: Simplify the numerator if possible. $\newline$ In this case, the numerator $3x^2 - 10$ cannot be simplified further because there are no common factors.
Check for further simplification: Check if the fraction can be simplified further. $\newline$ Since there are no common factors between the numerator and the denominator, the fraction is already in its simplest form.