Subtract the following rational expressions and write the difference in simplest form if possible.
$\frac{x^2}{x^2-25}-\frac{5x}{25-x^2}$

• A. $\(\frac{x}{x+5}\)$
• B. $\(\frac{x}{x-5}\)$
• C. $\(\frac{x}{\left(x-5\right)\left(x+5\right)}\)$
• D. $\(\frac{x+5}{x-5}\)$

Answer: (B)

Verified step by step guidance

1. Identify the given rational expressions: \(\frac{x^2}{x^2 - 25} - \frac{5x}{25 - x^2}\).
2. Recognize that the denominators \(x^2 - 25\) and \$25 - x^2\( are related by a negative sign, since \)25 - x^2 = -(x^2 - 25)\(. Rewrite the second fraction to have the denominator \)x^2 - 25$ by factoring out the negative sign: \(\frac{5x}{25 - x^2} = -\frac{5x}{x^2 - 25}\).
3. Rewrite the expression as \(\frac{x^2}{x^2 - 25} - \left(-\frac{5x}{x^2 - 25}\right)\), which simplifies to \(\frac{x^2}{x^2 - 25} + \frac{5x}{x^2 - 25}\).
4. Since the denominators are now the same, combine the numerators over the common denominator: \(\frac{x^2 + 5x}{x^2 - 25}\).
5. Factor the denominator as a difference of squares: \(x^2 - 25 = (x - 5)(x + 5)\), and factor the numerator by factoring out the common factor \(x\): \(x(x + 5)\). Then simplify the fraction by canceling common factors if possible.