Question

q1 simplify the expression.
\\(\frac{p^2 - 8p + 15}{p^2 - 6p + 9}\\)
\\(\frac{p^2 - 8p - 15}{p^2 - 6p + 9}\\)
\\(p - 5\\)
\\(\frac{p - 5}{p - 3}\\)
\\(\frac{p - 5}{p + 3}\\)

Explanation:

Step1: Factor numerator and denominator

Factor \( p^2 - 8p + 15 \): find two numbers that multiply to 15 and add to -8, which are -3 and -5. So \( p^2 - 8p + 15=(p - 3)(p - 5) \).
Factor \( p^2 - 6p + 9 \): it's a perfect square, \( p^2 - 6p + 9=(p - 3)^2 \).
Expression becomes \( \frac{(p - 3)(p - 5)}{(p - 3)^2} \).

Step2: Cancel common factors

Cancel one \( (p - 3) \) from numerator and denominator: \( \frac{(p - 5)}{(p - 3)} \).

Answer:

\(\boldsymbol{\frac{p - 5}{p - 3}}\) (corresponding to the option with this expression)