1.
a) (y²+y)/y²=y*(y+1)/y²=(y+1)/y.
b) (a²-2a)/(a²-4)=a*(a-2)/((a+2)(a-2)=a/(a+2).
2.
a) (3/a)+(a-3)/(a+5)=(3*(a+5)+a*(a-3))/(a*(a+5))=(3a+15+a²-3a)(a²+5a)=
=(a²+15)/(a²+5a).
b) 2x²/(x²-4)-2x/(x+2)=2x²/((x+2)(x-2)+2x/(x+2)=
=(2x²-2x*(x-2))/(x²-4)=(2x²-2x²+4x)/(x²-4)=4x/(x²-4).
3.
a) (a²-6a+9)/(y²-9)=(a-3)²/((y-3)(a+3))=(a-3)/(a+3).
b) (10y-30)/(y²+3y)=10*(y-3)/(y*(y+3)).
c) (a-3)/(a+3):(10*(y-3)/(y*(y+3))=y*(a-3)(a+3)/(10*(y-3)(y+3))=y/10.
4.
x/y=a y/z=1/a x/z=?
x=a*y z=a*y
x/z=a*y/(a*y)
x/z=1.