Question

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Answer 1

1)
x/(x²-6x+9) : [1/(3+x)-1/(3-x)-3x(x²-9)]=
=x/(x-3)² : [1/(x+3)+1/(x-3)-3x(x-3)(x+3)]=
=x/(x-3)² : (-x)/(x-3)(x+3)=
=x/(x-3)² × (x-3)(x+3)/(-x)=
=1/(x-3) × (x+3)/(-1)=
=(x+3)/(3-x)=
=(3+x)/(3-x)

2)
[1+7/(a-3)][(a+5)/(a²-a-12) +a/(a+4) -4/(a-3)](3-a)²=

a²-a-12 =a²-4a+3a-12=a(a-4)+3(a-4)=(a-4)(a+3)

=[1+7/(a-3)][(a+5)/(a+4)(a-3) +a/(a+4) -4/(a-3)](3-a)²=
=[(a-3+7)/(a-3)][(a+5)+a(a-3)-4(a+4)/(a+4)(a-3) ](3-a)²=
=[(a-3+7)/(a-3)][(a+5+a²-3a)-4a-16)/(a+4)(a-3) ](3-a)²=
=(a+4)/(a-3) × (a²-6a-11)/(a+4)(a-3) × (3-a)²=
= a²-6a-11