1. ## 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

2. Originally Posted by D7236
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

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 $\frac{(y-z)}{(y-z)}$

3. ## Thankyou

Ah, i see. Thank you so much