Question

simplify the expression completely if possible.
\\(\frac{x^2 - 10x + 24}{x^2 - 9x + 18}\\)

Explanation:

Step1: Factor numerator and denominator

Factor \(x^2 - 10x + 24\): Find two numbers that multiply to 24 and add to -10. Those numbers are -6 and -4. So, \(x^2 - 10x + 24=(x - 6)(x - 4)\).
Factor \(x^2 - 9x + 18\): Find two numbers that multiply to 18 and add to -9. Those numbers are -6 and -3. So, \(x^2 - 9x + 18=(x - 6)(x - 3)\).

Step2: Cancel common factors

The expression becomes \(\frac{(x - 6)(x - 4)}{(x - 6)(x - 3)}\). Cancel the common factor \((x - 6)\) (assuming \(x
eq6\) to avoid division by zero).

Answer:

\(\frac{x - 4}{x - 3}\) (for \(x
eq6\) and \(x
eq3\))