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Simplify: 1/(x-y)(x-z) + 1/(y-z)(x-z)I thought it wass a partial fraction. However, it...

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kismiskurma8 | Student, Undergraduate | eNotes Newbie

Posted November 12, 2012 at 9:40 AM via web

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Simplify: 1/(x-y)(x-z) + 1/(y-z)(x-z)

I thought it wass a partial fraction. However, it is not since the second denominator has no x, (y-z).

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durbanville | High School Teacher | (Level 1) Educator Emeritus

Posted November 12, 2012 at 10:28 AM (Answer #1)

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 `1/((x-y)(x-z)) + 1/((y-z)(x-z))`

Find the lowest common denominator (LCD): (x-y)(x-z)(y-z)

Apply the LCD to each part of the fraction:

= ``

Remove the brackets from the numerator:

= ``

The 'y' will cancel out from the numerator

= ``

Rearrange the numerator:

= ``

The (x-z) from the numerator cross cancels with the denominator

= `1/((x-y)(y-z))`

= 1/(x-y)(y-z)

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