Answer:
x - 2
Step-by-step explanation:
Given
[tex]\frac{(x-1)(x-2)(x^2-9x+14)}{(x-7)(x^2-3x+2)}[/tex]
Factor the quadratics on the numerator and denominator
x² - 9x + 14 = (x - 7)(x - 2)
x² - 3x + 2 = (x - 1)(x - 2)
The expression can now be rewritten as
[tex]\frac{(x-1)x-2)(x-7)(x-2)}{(x-7)(x-1)(x-2)\\}[/tex]
Cancel the common factors (x - 1), ( x - 2) and (x - 7) on numerator/ denominator, leaving
x - 2 ← in simplest form
