Are you good at manipulating?

Algebra Level 2

\[x=\dfrac {a-b}{a+b} \quad,\quad y=\dfrac {b-c}{b+c}\quad,\quad z=\dfrac {c-a}{c+a}.\]

If \(x,y\) and \(z\) satisfy the equations above, then express \[\dfrac {(1+x)(1+y)(1+z)}{(1-x)(1-y)(1-z)}\]

in terms of \(a,b\) and \(c\).

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