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How do you simpilfy this equation?: a-b/b^2  /  a^2-b^2/b

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rosey-girl | Student, Grade 12 | Valedictorian

Posted May 9, 2013 at 12:29 AM via web

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How do you simpilfy this equation?:

a-b/b^2  /  a^2-b^2/b

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

Posted May 9, 2013 at 12:57 AM (Answer #1)

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We can first factor the a^2 - b^2. 

`((a - b)/(b^2))/(((a-b)(a+b))/b)`

When dividing rational expression we flip the bottom, and proceed on multiplication. 

`((a - b)/b^2)/((a - b)(a + b)/b) = ((a - b)/b^2) *(b/((a - b)(a + b)))`

We can cancel common factor on top and bottom. 

`((a - b)/b^2)*(b/((a - b)(a+b))) = 1/(b(a+b))`

Hence, final answer is 1/(b(a + b)).

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oldnick | Valedictorian

Posted May 9, 2013 at 1:33 AM (Answer #2)

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`((a-b)/b^2)/((a^2-b^2)/b)= ` `(a-b)/b^2 xx b/((a+b)(a-b))=` `1/(b(a+b))`

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