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