Hyperbolic Function Identities

Hey, I'm having a hell of a time trying to figure out this simplification; If anyone has any input, it would be greatly appreciated!

Quote:

Show that: $\displaystyle \frac{sinh(3t)}{sinh(t)} = 1 + 2 cosh(2t) \ for \ t \neq 0$

I've tried breaking the $\displaystyle \frac{sinh(3t)}{sinh(t)}$ side down by turning it into $\displaystyle \frac{sinh (2t+t)}{sinh t}$ and using the $\displaystyle sinh (t+u)$ identity, but everything i do just seems to complicate the whole deal by expanding it to huge proportions that doesn't chop down any.

Any ideas on a hot identity to try? I'm not sure how else to approach this.