(x-1)/(x^2-5x+6)+(x-2)/(x^2-4x+3)+(x-3)/(x^2-3x+2)

(x-1)/(x^2-5x+6)+(x-2)/(x^2-4x+3)+(x-3)/(x^2-3x+2)
= (x-1)/{(x-2)(x-3)} + (x-2)/{x-1)(x-3)} + (x-3)/{(x-1)(x-2)}
= { (x-1)^2 + (x-2)^2 + (x-3)^2 } / { (x-1)(x-2)(x-3) }
= (x^2-2x+1+x^2-4x+4+x^2-6x+9) / { (x-1)(x-2)(x-3) }
= (3x^2-12x+14) / (x-1)(x-2)(x-3)
(1-4x)^2/(2x+3) * (4x^2+12x+9)/(4x^2-1)
= (4x-1)^2/(2x+3) * (2x+3)^2/(4x-1)
= (4x-1) * (2x+3)
= 8x^2+10x-3