1.(x^2-9y^2):(x+3y)= (x-3y)(x+3y):(x+3y)=x-3y

2.(a+2b):(a^2+4ab+4b^2)=(a+2b):(a+2b)^2=1:(a+2b)

3. (m^2-n^2):(mn-n^2)=(m-n)(m+n):n(m-n)=(m+n):n

4.(ax-ay):(x^2-2xy+y^2)=a(x-y):(x-y)^2=a:(x-y)  

5.(2ab-6a):(b^2-6b+9)=2a(b-3):(b-3)^2=2a:(b-3)

6. (5n^2+10n):(n^2-4)=5n(n+2):(n-2)(n+2)=5n:(n-2)

1)(x²-9y²):(x+3y)=(x²-(3y)²):(x+3y)=(x+3y)(x-3y):(x+3y)=x-3y, x≠-3y

2)(a+2b):(a²+4ab+4b²)=(a+2b):(a+2b)²=1/(a+2b) , a≠-2b

3)(m²-n²):(mn-n²)=(m+n)(m-n):n(m-n)=(m+n):n , n≠0,m≠n

4)(ax-ay):(x²-2xy+y²)=a(x-y):(x-y)²=a:(x-y) , x≠y

5)(2ab-6a):(b²-6b+9)=2a(b-3):(b-3)²=2a:(b-3) , b≠3

6)(5n²+10n):(n²-4)=5n(n+2):(n+2)(n-2)=5n:(n-2) , n≠2