Perform the indicated operations: (y^3+4y^2-54/y^2-2y+1) ÷ (y^2+y-2/y^4+8y) × (y-4/y^2-2y+4)

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The result of (y^3+4y^2-54/y^2-2y+1) ÷ (y^2+y-2/y^4+8y) × (y-4/y^2-2y+4) has to be determined.

(y^3+4y^2-54/y^2-2y+1) ÷ (y^2+y-2/y^4+8y) × (y-4/y^2-2y+4)

=> `((y^3+4y^2-54)/(y^2-2y+1))*((y^4+8y)/(y^2+y-2))*((y-4)/(y^2-2y+4))`

=> `((y^3+4y^2-54)(y^4+8y)(y-4))/((y^2-2y+1)(y^2+y-2)(y^2-2y+4))`

=> `((y^3+4y^2-54)y(y+2)(y^2-2*y+4)(y-4))/((y^2-2y+1)(y-1)(y+2)(y^2-2y+4))`

=> `((y^3+4y^2-54)y(y-4))/((y^2-2y+1)(y-1))`

=> `(y(y - 4)(y^3 + 4y^2 - 54))/((y^2 - 2y + 1)(y - 1))` ` `

` `**The result of ((y^3+4y^2-54)/(y^2-2y+1)) ÷ ((y^2+y-2)/(y^4+8y)) × ((y-4)/(y^2-2y+4)) is `(y(y - 4)(y^3 + 4y^2 - 54))/((y^2 - 2y + 1)(y - 1))`**

please simplify the answer

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