a) (x²-6x+9)/(x²-9) =(x-3)²/(x-3)(x+3) =(x-3)/(x+3)
b) (x²+8x+12)/(x²+7x+6)=(x+2)(x+6)/(x+1)(x+6)=(x+2)/(x+1)
c) (4-x²)/(x²-5x+4)=(2-x)(2+x)/(x-4)(x-1)
d) (x²+3x+4)/(x²-5x+4)=(x²+3x+4)/(x-4)(x-1)
e) (9-x²)/(x²-8x+15)=(3-x)(3+x)/(x-5)(x-3)=(3+x)/(x-5)(-1)=(3+x)/(5-x)
f)(x²-x)/(x²-2x+1)=x(x-1)/(x-1)²=x/(x-1)
g) [x(x-2)+1]/(x²+2x-3)=(x²-2x+1)/(x²+2x-3)=(x-1)²/(x-1)(x+3)=(x-1)/(x+3)
h) (x²-x-6)/[(x-4)²+(x-4)]=(x-3)(x+2)/(x²-8x+16+x-4)=(x-3)(x+2)/(x²-7x+12)=
=(x-3)(x+2)/(x-4)(x-3)=(x+2)/(x-4)
i) [(x-2)²-x+2]/[(x-3)²-1]=(x²-4x+4-x+2)/(x-3-1)(x-3+1)=(x²-5x+6)/(x-4)(x-2)=
=(x-3)(x-2)/(x-4)(x-2)=(x-3)/(x-4)