Factor this please quick!

**Proof_of_life** · November 7th 2008, 09:05 AM

$T(z) = \frac{z}{2-z}$

$S^{-1}(z) = 4\frac{z-1}{z+4}$

Solve:

$L(z) = S^{-1}(T(z))$

Can someone show me the steps? I know to plug in for z but I can't seem to do it the right way...

**Proof_of_life** · November 7th 2008, 09:18 AM

For Linear Functional Transformations. Thanks Moo, you just put a negative for the 4 instead of a positive when factoring out tho. James has the correct answer..

**james_bond** · November 7th 2008, 09:38 AM

Repost, sorry I thought mine was wrong and Moo wrote it more nicely by the way.
$L(z) = S^{-1}(T(z))=S^{-1}\left(\frac{z}{2-z}\right)=4\frac{\frac{z}{2-z}-1}{\frac{z}{2-z}+4}=-\frac{8 (-1+z)}{-8+3 z}$
$z\ne 2\,\text{and}\, \frac 83$

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