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?

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- Jan 31st 2006, 10:06 AMone_passerbyexpressing in terms
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? - Jan 31st 2006, 10:15 AMThePerfectHackerQuote:

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.