Subtract the rational expressions \(\frac{5x}{x + 2}\) and \(\frac{3x}{x - 2}\)

Step 1 ：Find a common denominator. The least common denominator (LCD) of \(x + 2\) and \(x - 2\) is \((x + 2)(x - 2)\) or \(x^2 - 4\)

Step 2 ：Rewrite each fraction with the LCD as the denominator. This gives us \(\frac{5x(x - 2)}{x^2 - 4} - \frac{3x(x + 2)}{x^2 - 4}\)

Step 3 ：Subtract the fractions now that they have the same denominator. This gives us \(\frac{5x(x - 2) - 3x(x + 2)}{x^2 - 4}\)

Step 4 ：Simplify the numerator, which results in \(\frac{5x^2 - 10x - 3x^2 - 6x}{x^2 - 4}\)

Step 5 ：Combine like terms in the numerator to get \(\frac{2x^2 - 16x}{x^2 - 4}\)

Step 6 ：Finally, break down the numerator and denominator to their simplest terms. This gives us \(\frac{2x(x - 8)}{(x - 2)(x + 2)}\)