Answer:
[tex] \frac{(y-x)^2}{(x-y)^2} \frac{(x-z)^2}{(z-x)^2}\frac{(z-y)^2}{(y-z)^2} =1[/tex]
And on this case the samllest possible value would be 1
Step-by-step explanation:
For this case we have the following expression:
[tex] \frac{(y-x)^2}{(y-z)(z-x)} \frac{(z-y)^2}{(z-x)(x-y)} \frac{(x-z)^2}{(x-y)(y-z)}[/tex]
And we can rewrite this expression like this:
[tex] \frac{(y-x)^2}{(x-y)^2} \frac{(x-z)^2}{(z-x)^2}\frac{(z-y)^2}{(y-z)^2}[/tex]
For this case is important to remember the following property from algebra:
[tex] (a-b)^2 = a^2 -2ab + b^2 [/tex]
[tex] (b-a)^2 = b^2 - 2ab + a^2[/tex]
On this case we can see that [tex] (a-b)^2 = (b-a)^2[/tex]
So then [tex] (y-x)^2 = (x-y)^2 , (x-z)^2= (z-x)^2, (z-y)^2 =(y-z)^2 [/tex]
So then we can simplify all the expression and we got this:
[tex] \frac{(y-x)^2}{(x-y)^2} \frac{(x-z)^2}{(z-x)^2}\frac{(z-y)^2}{(y-z)^2} =1[/tex]
And on this case the samllest possible value would be 1
