[tex]\frac{x^2-5x+6}{x^2-4x+4} =\frac{x+a}{x+b} [/tex]
[tex]x^{2} -5x+6=0 [/tex]
Δ=b²-4ac= (-5)²-4×1×6= 25-24=1
==> x1= (-b+√Δ)/2a = (-(-5)+√1)/2 = (5+1)/2 = 6/2 = 3
x²= (-b-√Δ)/2a= (-(-5)-√1)/2 = (5-1)/2 = 4/2 =2
[tex]==> x^2-5x+6 = (x-2)(x-3) [/tex]
[tex]x^{2} -4x+4= (x-2)^2 [/tex]
[tex]\frac{(x-2)(x-3)}{(x-2)^2} =\frac{x+a}{x+b} [/tex]
[tex]\frac{x-3}{x-2} =\frac{x+a}{x+b} [/tex]
a= -3
b= -2
