Question

what is the common denominator of \\(\frac{5}{x^2 - 4} - \frac{2}{x + 2}\\) in the complex fraction \\(\frac{\frac{2}{x - 2} - \frac{3}{x^2 - 4}}{\frac{5}{x^2 - 4} - \frac{2}{x + 2}}\\)? \\(\bigcirc\\ (x + 2)(x - 2)\\) \\(\bigcirc\\ x - 2\\) \\(\bigcirc\\ (x + 2)^2(x - 2)\\) \\(\bigcirc\\ x + 2\\)

Explanation:

Step1: Factor quadratic denominator

$x^2-4=(x+2)(x-2)$

Step2: List all denominators

Denominators: $x^2-4=(x+2)(x-2)$, $x+2$, $x-2$

Step3: Identify common denominator

The least common multiple of $(x+2)(x-2)$, $x+2$, $x-2$ is $(x+2)(x-2)$

Answer:

A. $(x + 2)(x - 2)$