2
x²-18x+11=0
x1+x2=18,x1*x2=11,
x1²+x2²=(x1+x2)²-2x1*x2=324-22=302
x2/(x2²-1)+x1/(x1²-1)=(x1²x2-x2+x1x2²-x1)/(x2²*x1²-x2²-x1²+1)=
=[x1x2(x1+x2)-(x1+x2)]/[(x1x2)²-(x1²+x2²)+1]=
=(x1+x2)(x1x2-1)/[(x1x2)²-(x1²+x2²)+1]=18*10/(121-302+1)=
=180/(-180)=-1
1
x²+9x+13=0
x1+x2=-9 , x1*x2=13
x1²+x2²=(x1+x2)²-2x1x2=81-26=55
x2/(2x2-x1)+x1/(2x1-x2)=(2x1x2-x1²+2x1x²-x2²)/(2x2-x1)(2x1-x2)=
=[4x1x2-(x2²+x1²)]/(4x1x2-2x2²-2x1²+x1x2)=
=[4x1x2-(x2²+x1²)]/[5x1x2-2(x1²+x2²)]=(52-55)/(65-110)=-3/(-45)=1/15