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

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The discussion revolves around the algebraic identity 1/k + 1/(1-k) = 1/(k(1-k)). The original poster expresses confusion about manipulating these expressions but realizes the answer shortly after posting. They acknowledge a momentary lapse in basic arithmetic and apologize for the confusion. Other participants empathize, noting that similar moments of clarity often occur while explaining problems. The conversation highlights the common experience of struggling with math concepts, especially when tired.
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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...
 
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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!
 
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...
 

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