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Math Help - Help with simplifying?

  1. #1
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    Unhappy Help with simplifying?

    simplify x/(y-x)(z-x) + y/(z-y)(x-y) + z/(x-z)(y-z)

    *Hint: the common denominator consists of 3 factors only

    Please show all important steps
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  2. #2
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    Quote Originally Posted by D7236 View Post
    simplify x/(y-x)(z-x) + y/(z-y)(x-y) + z/(x-z)(y-z)

    *Hint: the common denominator consists of 3 factors only

    Please show all important steps
    You need to change the sign on some of the factors, so the factor is the same in each fraction,

    for instance

    (y-x)=-(x-y),\ (z-x)=-(x-z),\ (z-y)=-(y-z)

    \frac{x}{(y-x)(z-x)}+\frac{y}{(z-y)(x-y)}+\frac{z}{(x-z)(y-z)}

    =\frac{x}{(x-y)(x-z)}+\frac{-y}{(x-y)(y-z)}+\frac{z}{(x-z)(y-z)}

    Next you check which fractions have which factor missing, then multiply the fraction by

    \frac{missing\ factor}{missing\ factor}

    for example, the first fraction must be multiplied by \frac{(y-z)}{(y-z)}
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  3. #3
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    Thankyou

    Ah, i see. Thank you so much
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