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What is a^2-b^2/a-b reduced to its lowest terms.

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hess45 | Student, College Freshman | eNotes Newbie

Posted February 28, 2009 at 10:47 AM via web

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What is a^2-b^2/a-b reduced to its lowest terms.

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kborgeson | Middle School Teacher | (Level 2) Adjunct Educator

Posted March 22, 2009 at 1:15 AM (Answer #1)

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a^2 - b^2 is the difference of two perfect squares.  When you have the difference of two squares they can factor into two binomials (a + b)(a - b). 

Your problem then looks like: (a + b)(a - b)/(a - b).   Since it is a division you can then cancel the two binomials that are (a - b). 

This leaves you with the answer:  a + b.  :)

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lynn30k | High School Teacher | (Level 3) Associate Educator

Posted March 1, 2009 at 12:30 AM (Answer #2)

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First, you must figure out another way of writing your numerator, a^2-b^2. You can factor this to (a+b)(a-b); those terms, when multiplied, give you your original numerator, because when you multiply them, the ab terms cancel out (one is positive, one is negative.) You then have

(a+b)(a-b)/a-b

Because your terms in the numerator are multiplied by each other, the a-b terms, one in the numerator and one in the denominator equal one, and you are left with a+b as your answer.

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