Answer:
Step-by-step explanation:
Factorize x² - 5x + 6
x² - 5x + 6 = x² - 3x - 2x + 6
= x(x - 3) - 2(x - 3)
= (x - 3)(x -2)
[tex]\sf \dfrac{(x -1)}{4x -8} \ \div \dfrac{x-2}{x^2-5x + 6} = \dfrac{x -1 }{4x-8} * \dfrac{x^2 - 5x + 6}{x -2}[/tex]
[tex]\sf = \dfrac{(x -1)}{4x-8)}*\dfrac{(x-3)(x-2)}{(x-2)}\\\\ [\text{\bf (x-2) in the numerator and denominator will be cancelled}]\\\\\\= \dfrac{(x -1)(x-3)}{4x-8}\\\\=\dfrac{x*x + x*(-3) + (-1)*x + (-1)*(-3)}{4x-8}\\\\=\dfrac{x^2-3x -x + 3}{4x -8}\\\\=\dfrac{x^2-4x +3}{4x-8}[/tex]
