🚀 go-pugleaf

I'm having huge problems getting an extremely long equation
to typeset correctly using TeXtures on the Mac.  Here's
the situation.  Warning:  This post is rather long due
to the fact that I've included all the error messages
and stuff I got when trying to typeset this formula.
Here's your chance to bail out if you don't think
you'll be able to help:

The formula should eventually come out looking something
like this (simplified for ascii):

[xx(x)] = fraction {stuff (x) 
	+ (stuff) fraction {stuff[x(xx)]}
	- fraction stuff [x(xx)]}		(40)
	  at 0 < x 1

Obviously that's very simplified, but you get the idea.
Notice the one set of braces that runs from the first
line through the end of the third line.  That's the part
that's keeping me from just breaking the darn thing up 
into four separate $$ lines.

If I typeset it straight, it runs off the end of the page
and I get an "overfull hbox" error message, but it *does*
typeset.

Here's what it looks like typeset straight, with no attempts
to break up the line:

$$[C_{av}(t)]_{x=1} = {1 \over {1+N_M}} \left\{1 +N_M-\exp(-N_M) 
+ (2-{\fr {N_M} {N_M-K_f}})  {{N_M\exp(-N_M)} \over {N_M - K_f}}
\br{1-\exp[t(N_M-K_f)]} - {{N^2_Mt\exp(-N_M)} \over {N_M - K_f}} 
K_f\exp [t(N_M-K_f)]\right\} \qquad{\rm at\ } 0\le t\le 1 
\eqno (40)$$

I've tried both \displaylines and \eqalign to get the lines to
break and both give me "missing bracket" type error messages.

Here's how I tried to do it with \eqalign:

$$\eqalign{[C_{av}(t)]_{x=1} 
&= {1 \over {1+N_M}} \left\{1+N_M-\exp(-N_M)  \cr
&+ (2-{\fr {N_M} {N_M-K_f}})  {{N_M\exp(-N_M)}
\over {N_M - K_f}}  \br{1-\exp[t(N_M-K_f)]}  \cr
&- {{N^2_Mt\exp(-N_M)}
\over {N_M - K_f}}  K_f\exp [t(N_M-K_f)]\right\} \cr
&\qquad{\rm at\ } 0 \le t \le 1  \cr} \eqno (40)$$

And here's the error message I got:

! Extra }, or forgotten \right.
<template> }
            $\hfil \endtemplate 
<argument> ...M-\exp (-N_M) \cr 
                                &+ (2-{\fr {N_M} {N_M-K_f}}) ...
\eqalign ...{}##}$\hfil \crcr #1
                                \crcr }}\,
l.147 ...\ } 0 \le t \le 1  \cr}
                                 \eqno (40)$$

I don't understand this because the only brackets I added
from when it did typeset were those at the beginning and end of
the \eqalign.

So I tried \displaylines.  Here's how it looked:

$$\displaylines{[C_{av}(t)]_{x=1} = {1 \over {1+N_M}}
\left\{1+N_M-\exp(-N_M)  \cr + (2-{\fr {N_M} {N_M-K_f}}) 
{{N_M\exp(-N_M)} \over {N_M - K_f}}  \br{1-\exp[t(N_M-K_f)]}  \cr
- {{N^2_Mt\exp(-N_M)} \over {N_M - K_f}}  K_f\exp
[t(N_M-K_f)]\right\} \cr \qquad{\rm at\ } 0 \le t \le 1  \cr}
 \eqno (40)$$

And here's the error message I got:

! Missing \right. inserted.
<inserted text> 
                \right .
<to be read again> 
                   $
<template> \hfil $
                  }\endtemplate 
<argument> ...M-\exp (-N_M) \cr 
                                + (2-{\fr {N_M} {N_M-K_f}}) {...
\displaylines ...hfil $}\crcr #1
                                \crcr }
l.145 ...\ } 0 \le t \le 1  \cr}

As far as I can tell, I set both of these up exactly as the
examples in the TeXBook by Knuth.  But as you can see, they're 
not working.  What am I doing wrong and how do I fix it?
Thanks for your help!

	Caren Levine
	Univ. of Michigan
	College of Engineering
	(313) 764-4906
	caren@engin.umich.edu

P.S.  Sorry for the long post, I wanted those helping me to have
as much information as possible to be able to help solve the
problem.