Question

1. divide

\\(\frac{x + 5}{x - 6} \div \frac{x - 2}{x^2 - x - 30}\\)
options:
\\(\frac{1}{x - 2}\\)
\\(\frac{(x + 5)(x + 5)}{x - 2}\\)
\\(x - 2\\)
\\(\frac{x - 2}{(x - 6)(x - 6)}\\)

Explanation:

Step1: Convert division to multiplication

$\frac{x+5}{x-6} \times \frac{x^2 - x - 30}{x-2}$

Step2: Factor the quadratic

$x^2 - x - 30 = (x-6)(x+5)$

Step3: Substitute and simplify

$\frac{x+5}{x-6} \times \frac{(x-6)(x+5)}{x-2} = \frac{(x+5)(x+5)}{x-2}$

Answer:

$\frac{(x+5)(x+5)}{x-2}$ (second option)