Why does 1/k + 1/(1-k) = 1/k(1-k)?

[quozzy]

Okay, I feel stupid posting this, but algebraic manipulation is failing me. I know these two expressions are the same, but can anyone help me see how one could arrive at one of these from the other?

EDIT: *facepalm* Alright, I was trying to figure this out for a half hour before I posted. Of course, after posting I immediately came across the answer. I guess it was just a minor brainfart. Sorry guys, don't mind me...

 

[Hurkyl]

I assume you meant 1/(k(1-k)) on the right hand side.

I also assume you know how to compute with fractions, such as writing:

$$\frac{1}{3} - \frac{1}{4}$$​

as a single fraction. So, can you explain why you are having trouble with the question you asked? Where are you stuck?

EDIT: *facepalm* Alright, I was trying to figure this out for a half hour before I posted. Of course, after posting I immediately came across the answer. I guess it was just a minor brainfart. Sorry guys, don't mind me...

Ah! Good then. Brainfarts happen all the time. You wouldn't believe how often I solve a problem in the process of trying to explain it to someone else as I'm asking for help!

 

[quozzy]

Yeah, I realize now how silly this question really was. As I pointed out in my edit, for some reason I completely blanked out on basic arithmetic. I guess that's what happens when you're overdue for a good night's sleep...