Hello! I came across a probem that I'm stuck on! It is If \(x+\frac{1}{y}=1\) and \(y+\frac{1}{z}=1\), what is the value of the product \(xyz\)?

Do you have to expand or square it! Thanks!

x + 1/y = 1

x = 1 - 1/y = [ y - 1] / y

And

y + 1/z = 1

1/z = 1 - y which implies that

z = 1 / [ 1 - y]

So x y z =

( [ y - 1] / y ) * y * [ 1 / ( 1 - y) ] =

[ y - 1 ] * [ 1 / (1 - y) ] =

-1 ( 1 - y) * [ 1 / (1 - y) ] =

-1

Thank you, CPhill! I understand it better, now!