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 to subtract: \(\frac{x^2}{x^2 - 25} - \frac{5x}{25 - x^2}\).
2. Notice that the denominators \(x^2 - 25\) and \$25 - x^2\( are related. Factor \)x^2 - 25\( as \)(x - 5)(x + 5)\(, and recognize that \)25 - x^2 = -(x^2 - 25) = -(x - 5)(x + 5)$.
3. Rewrite the second fraction to have the same denominator as the first by factoring out the negative sign: \(\frac{5x}{25 - x^2} = \frac{5x}{-(x - 5)(x + 5)} = -\frac{5x}{(x - 5)(x + 5)}\).
4. Now express the subtraction as \(\frac{x^2}{(x - 5)(x + 5)} - \left(-\frac{5x}{(x - 5)(x + 5)}\right)\), which simplifies to \(\frac{x^2}{(x - 5)(x + 5)} + \frac{5x}{(x - 5)(x + 5)}\).
5. Since the denominators are the same, combine the numerators: \(\frac{x^2 + 5x}{(x - 5)(x + 5)}\). Then factor the numerator if possible and simplify the expression by canceling common factors.