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

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

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Multiplication with rational exponents

Full solution

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

\newline

\frac{5}{3 x}-\frac{3 x}{5}

\newline

Answer:

Identify Common Denominator: Identify a common denominator for the two fractions. The common denominator for the fractions $(\frac{5}{3x})$ and $(\frac{3x}{5})$ is the product of the two denominators, which is $3x \times 5 = 15x$ .
Rewrite with Common Denominator: Rewrite each fraction with the common denominator. $\newline$ To rewrite $\frac{5}{3x}$ with the common denominator $15x$ , we multiply the numerator and denominator by $5$ . For $\frac{3x}{5}$ , we multiply the numerator and denominator by $3x$ . $\newline$ $\frac{5}{3x} \times \frac{5}{5} - \frac{3x}{5} \times \frac{3x}{3x} = \frac{25}{15x} - \frac{9x^2}{15x}$
Combine Fractions: Combine the fractions over the common denominator. $\newline$ Now that both fractions have the same denominator, we can combine them into a single fraction. $\newline$ $(\frac{25}{15x}) - (\frac{9x^2}{15x}) = \frac{25 - 9x^2}{15x}$
Simplify Numerator: Simplify the numerator if possible. $\newline$ In this case, the numerator $25 - 9x^2$ cannot be factored or simplified further.
Check for Further Simplification: Check if the fraction can be simplified. The fraction $(25 - 9x^2)/(15x)$ cannot be simplified further because the numerator and denominator do not have any common factors other than $1$ .

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