Question 301998
[(y^3 + 9y) / (y^2 +2y - 35)] ÷ [(y^2-81) / (y^2 -14y + 45)]

Factorise various brackets:
y^3 + 9y = y(y^2 + 9)
y^2 +2y - 35 = (y+7)(y-5)
y^2-81 = (y+9)(y-9)
y^2 -14y + 45 = (y-9)(y-5)

Put the factorised brackets back to the question and change the question to multiplication:

[y(y^2+9)]/[(y+7)(y-5)] * [(y-9)(y-5)]/[(y+9)(y-9)]

cancel out "(y-9)" and "(y-5)"

This gives: 

y(y^2+9)/[(y+7)(y+9)]