Question

question
simplify the following expression completely:
\\(\frac{x^2 - 10x + 25}{x^2 - 8x + 15}\\)
answer attempt 1 out of 2

Explanation:

Step1: Factor numerator and denominator

Factor \(x^2 - 10x + 25\) using perfect square formula: \(x^2 - 10x + 25=(x - 5)^2\).
Factor \(x^2 - 8x + 15\) by finding two numbers that multiply to 15 and add to -8: \(x^2 - 8x + 15=(x - 3)(x - 5)\).
So the expression becomes \(\frac{(x - 5)^2}{(x - 3)(x - 5)}\).

Step2: Cancel common factors

Cancel the common factor \((x - 5)\) from numerator and denominator (assuming \(x
eq5\) to avoid division by zero).
We get \(\frac{x - 5}{x - 3}\).

Answer:

\(\frac{x - 5}{x - 3}\)