expressing in terms

Quote:

Originally Posted by one_passerby

I can't seem to get an answer to this question:
x= a + (1/y) , y= a - (1/z) where a is constant.

Express z in terms of a and x only

anyone?

You are given that,
$x=a+\frac{1}{y}$ (1)
$y=a-\frac{1}{z}$ (2)

Using equation (2) thus,
$z=\frac{1}{a-y}$
Now using equation (1) we get that,
$y=\frac{1}{x-a}$ .
Substitute $y$ from (1) into (2),
$z=\frac{1}{a-\frac{1}{x-a}}$
Simplify this complex fraction,
$z=\frac{x-a}{ax-a^2-1}$
Q.E.D.