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What is the LCD and sum of `2/(x^2-18)+2/(x+6)?`

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monique06 | Valedictorian

Posted May 16, 2013 at 11:44 PM via web

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What is the LCD and sum of `2/(x^2-18)+2/(x+6)?`

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mjripalda | High School Teacher | (Level 3) Educator

Posted May 17, 2013 at 1:12 AM (Answer #1)

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Note that LCD is the product of the different factors in the denominators.

Since x^-18 is not factorable, the LCD of the given rational expressions is `(x^2-18)(x+6)` .

To take the sum, express the fractions with same denominator. So, use the LCD as their new denominator.

`2/(x^2-18)+2/(x+6)`

`=2/(x^2-18)*(x+6)/(x+6)+2/(x+6)*(x^2-18)/(x^2-18)`

`=(2x+12)/((x^2-18)(x+6))+(2x^2-36)/((x^2-18)(x+6))`

Now that they have same denominators, proceed to add.

`=(2x^2+2x-24)/((x^2-18)(x+6))`

Hence, the sum is` (2x^2+2x-24)/((x^2-18)(x+6))` .

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