Basic Algebra for transistors

[Patshat]

Hello
I ain't done Algebra in 50 years or more. I was reading up on npn transistors and came to a formula for gain.
I attached a pic of the equation. I can't figure out wher the '1' came from and what it represents.
Anybody enlighten me, by mabey going through the steps and explaining the process.

Thanks

 

[dick_freebird]

Just being fancy - alpha is shown (Ic/Ie) but
Ie = Ic+Ib, Ic is beta*Ib, so Ie is (1+beta)*Ib
and there's your "1".