1.
(y²-y)/y²=y*(y-1)/y²=(y-1)/y.
(a²-2a)/(a²-4)=a*(a-2)/((a-2)*(a+2))=a/(a+2).
2.
3/a+(a-3)/(a+5)=(3*(a+5)+a*(a-3))/(a*(a+5))=(3a+15+a²-3a)/(a*((a+5))=
=(a²+15)/(a²+5a).
2x²/(x²-4)-2x/(x+2)=(2x²/((x+2)*(x-2))=(2x²-2x*(x-2))/((x+2)*(x-2))=
(2x²-2x²+4x)/(x²-4)=4x/(x²-4)
3.
(y²-6y+9)/(y²-9):(10x-30)/(y²+3y)
1) (y²-6y+9)/(y²-9)=(y-3)²/((y-3)*(y+3))=(y-3)/(y+3).
2) (10x-30)/(y²+3y)=10*(x-3)/(y*(y+3)).
3) ((y-3)/(y+3)):(10*(x-3)/(y/(y+3))=(y-3)*y*(y+3)/((y+3)*10*(x-3))=y/10=70/10=7.
4.
x/y=a, y/z=1/a x/z - ?
y=z*a
x/(z/a)=a
x*a/z=a |÷a
x/z=1.