1) 15x^2y^6/9xy^4=5xy^2/3
2) 6x^2+18x^4/12x^3=6x^2(1+3x^2)/12x^3=1+3x^2/2x
3) 4x-16/x^2-16=4(x-4)/(x-4)(x+4)=4/x+4
2b+18/b^2+18b+81=2(b+9)/(b+9)^2=2/b+9
5)y^2-4y+4/4-y^2=(y-2)^2/(2-y)(2+y)= - y-2/2+y
6)a+1/a^2-2a+1=-(a-1)/(a-1)^2= - 1/(a-1)^2
7)x^2-1/x^3+1=(x-1)(x+1)/(x+1)(x^2-x+1)=x-1/x^-x+1