Verified answer

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.