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

$\frac{x}{x + 5}$

$\frac{x}{x - 5}$

$\frac{x}{(x - 5) (x + 5)}$

$\frac{x + 5}{x - 5}$

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Identify the given rational expressions: $\frac{x^2}{x^2 - 25} - \frac{5x}{25 - x^2}$.

Notice that the denominators $x^2 - 25$ and \$25 - x^2$ are related. Recall that $x^2 - 25$ factors as $(x - 5)(x + 5)$, and $25 - x^2$ is the negative of $x^2 - 25$, so $25 - x^2 = -(x^2 - 25) = -(x - 5)(x + 5)$.

Rewrite the second fraction to have the same denominator as the first by factoring out the negative sign: $\frac{5x}{25 - x^2} = \frac{5x}{-(x - 5)(x + 5)} = -\frac{5x}{(x - 5)(x + 5)}$.

Now express both fractions with the common denominator $(x - 5)(x + 5)$: the first fraction is $\frac{x^2}{(x - 5)(x + 5)}$, and the second is $-\frac{5x}{(x - 5)(x + 5)}$. The subtraction becomes $\frac{x^2}{(x - 5)(x + 5)} - \left(-\frac{5x}{(x - 5)(x + 5)}\right)$.

Combine the numerators over the common denominator: $\frac{x^2 + 5x}{(x - 5)(x + 5)}$. Then factor the numerator if possible and simplify the expression by canceling common factors.

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Subtract the following rational expressions and write the difference in simplest form if possible. x2x2−25−5x25−x2\(\frac{x^2}{x^2-25}\)-\(\frac{5x}{25-x^2}\)

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