Simplify the expression ((x-1)(x-2)(x^(2) -9x+14))/((x-7)(x^(2) -3x+2))

Question

Simplify the expression

`((x-1)(x-2)(x^(2) -9x+14))/((x-7)(x^(2) -3x+2))`

Answer 1

x - 2

Explanation:

Given

`((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

`((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