Question

X-1/4x-8 divided x-2/x2-5x+6

Answer 1

Explanation:

Factorize x² - 5x + 6

x² - 5x + 6 = x² - 3x - 2x + 6

= x(x - 3) - 2(x - 3)

= (x - 3)(x -2)

`\sf ((x -1))/(4x -8) \ / (x-2)/(x^2-5x + 6) = (x -1 )/(4x-8) * (x^2 - 5x + 6)/(x -2)`

`\sf = ((x -1))/(4x-8))*((x-3)(x-2))/((x-2))\\\\ [\text{\bf (x-2) in the numerator and denominator will be cancelled}]\\\\\\= ((x -1)(x-3))/(4x-8)\\\\=(x*x + x*(-3) + (-1)*x + (-1)*(-3))/(4x-8)\\\\=(x^2-3x -x + 3)/(4x -8)\\\\=(x^2-4x +3)/(4x-8)`