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Simplify this equation: (y-3)^2 / y^2-6y+9  /  y^2-9 / y^3-9y

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rosey-girl | Student, Grade 12 | (Level 1) Valedictorian

Posted May 15, 2013 at 9:38 PM via web

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Simplify this equation:

(y-3)^2 / y^2-6y+9  /  y^2-9 / y^3-9y

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violy | High School Teacher | (Level 3) Assistant Educator

Posted May 15, 2013 at 11:06 PM (Answer #1)

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We can first split the second rational expression and proceed to multiplication.

`(y - 3)^2/(y^2 - 6y + 9) *(y^3 - 9y)/(y^2 - 9)`

We can rewrite the top of the frist one as: (y - 3)(y - 3).

For the bottom of the first one, we can factor it as (y - 3)(y - 3)

For the top of the second one, we can first factor out a y.

`y^3 - 9y = y(y^2 - 9)`

So, we will have:

`((y - 3)(y - 3))/((y - 3)(y - 3)) * (y(y^2 - 9))/(y^2 - 9)`

Cancel common factor on top and bottom.

So, the final answer will just be equal to y.

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oldnick | (Level 1) Valedictorian

Posted May 15, 2013 at 11:16 PM (Answer #2)

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`((y-3)^2/(y^2-6y+9))/((y^2-9)/(y^3-9y))=` `((y-3)^2/(y-3)^2)/((y^2-9)/(y(y^2-9)))=` `1/(1/y)=y`

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