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

  • Thread starter quozzy
  • Start date
In summary, the conversation was about one person struggling with algebraic manipulation and asking for help. After realizing their mistake, they apologized for asking the question and acknowledged that they just had a minor brainfart. The other person reassured them that it's common to solve a problem while trying to explain it to someone else. The original person then explained their mistake was due to being tired.
  • #1
quozzy
15
0
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...
 
Mathematics news on Phys.org
  • #2
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:
[tex]\frac{1}{3} - \frac{1}{4}[/tex]​
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!
 
  • #3
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...
 

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

1. What is the formula for 1/k + 1/(1-k)?

The formula for 1/k + 1/(1-k) is 1/k(1-k).

2. Why does 1/k + 1/(1-k) equal 1/k(1-k)?

The two fractions, 1/k and 1/(1-k), have a common denominator of k(1-k). When we add them together, we follow the basic rule of adding fractions with the same denominator, which is to simply add the numerators and keep the common denominator. Therefore, 1/k + 1/(1-k) becomes (1+1)/(k(1-k)) = 2/k(1-k) = 1/k(1-k).

3. Can 1/k + 1/(1-k) be simplified further?

No, the fraction 1/k + 1/(1-k) is already in its simplest form, which is 1/k(1-k).

4. How is the formula 1/k + 1/(1-k) used in mathematics?

The formula 1/k + 1/(1-k) is commonly used in algebraic equations to simplify expressions or solve equations. It is also used in calculus to evaluate limits and perform other mathematical operations.

5. Is the formula 1/k + 1/(1-k) applicable to all values of k?

Yes, the formula 1/k + 1/(1-k) is applicable to all values of k except for k = 0 and k = 1. This is because the denominator k(1-k) becomes 0 when k = 0 or k = 1, which is undefined in mathematics.

Similar threads

What is the Stirling transform of (k-1)?
    • General Math
Replies
1
Views
1K
Is ceil(n/k) equal to floor((n-1)/k) + 1 for positive integer values of n and k?
    • Precalculus Mathematics Homework Help
Replies
2
Views
2K
I Why Lagrangian includes 1/2m by Landau?
    • Mechanics
Replies
24
Views
1K
MHB Solutions for arcsin(x) + arcsin(k) = π/2
    • General Math
Replies
5
Views
2K
How can I simplify [1-(k(sin^2) θ)] using trigonometric identities?
    • General Math
Replies
1
Views
2K
Relationship between ln k and 1/t using different formula
    • Chemistry
Replies
2
Views
6K
MHB Show Inequality: Explain Why $g(k) \geq \frac{3^k}{2k+1}$ in Football Matches
    • Set Theory, Logic, Probability, Statistics
Replies
7
Views
2K
Other Best resources for self-studying math from K-12?
    • Science and Math Textbooks
Replies
28
Views
3K
Calculating time to reduce alcohol in wine using heating method
    • Chemistry
4
Replies
131
Views
4K
Induction Proof, Apostol Calc Vol I, I.4.4.7
    • Calculus and Beyond Homework Help
Replies
6
Views
1K

Hot Threads

Recent Insights

Back
Top