Q42 Prep 3 Algebra Question Bank

a) Find n(X) in the simplest form, showing the domain of n: \[ n(X) = \frac{X^2 - 2X - 15}{X^2 - 9} \div \frac{2X - 10}{X^2 - 6X + 9} \]

(a) \( \frac{(X-3)}{2(X+3)} \), Domain: X ≠ -3, 3, 5

(b) \( \frac{(X+5)}{2(X+3)} \), Domain: X ≠ -3, 3

(c) \( \frac{1}{2}(X-3) \), Domain: X ≠ -3, 3, 5

(d) \( \frac{(X-3)^2}{2(X+3)(X-5)} \), Domain: X ≠ -3, 3, 5

Correct Answer:
\[ n(X) = \frac{1}{2}(X-3) \]
Domain of \( n = \mathbb{R} - \{-3, 3, 5\} \) (All real numbers except -3, 3, and 5)

MR/Nasef.N