Question

Simplify the expression
$\frac{(x-1)(x-2)(x^{2} -9x+14)}{(x-7)(x^{2} -3x+2)}$

Answer 1

Answer:

x - 2

Step-by-step explanation:

Given

$\frac{(x-1)(x-2)(x^2-9x+14)}{(x-7)(x^2-3x+2)}$

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

$\frac{(x-1)x-2)(x-7)(x-2)}{(x-7)(x-1)(x-2)\\}$

Cancel the common factors (x - 1), ( x - 2) and (x - 7) on numerator/ denominator, leaving

x - 2 ← in simplest form