MHB What Is a Common Denominator for These Fractions?

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To find a common denominator for the fractions in the expression, it's essential to factor the denominators: \( r^2 - 2r = r(r - 2) \) and \( r^2 - 4 = (r - 2)(r + 2) \). The common denominator can be determined by taking the product of the unique factors, which includes \( r \), \( (r - 2) \), and \( (r + 2) \). The discussion emphasizes the importance of clearly stating the problem and using typed equations for clarity. Understanding how to combine fractions using a common denominator is crucial for solving the expression correctly.
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Please help me solve this calculation
 

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Hi Khadeeja. Welcome to MHB. (Wave)

I can see

$\displaystyle \frac{r-1}{r^2-2r}-\frac{r-2}{r^2-4}+\frac{-2r}{r^2-2r} $

But then also there's $-1$ underneath that I'm not certain how it's connected to this expression.

It's not clear what you're asking as it stands. Could you post the full question/explain what you want to do?
 
I will assume that the "-1" MountEvariste is concerned about is from another problem.
(That's one of the many reasons why it is much better to type a problem in rather than post a picture.)

Do you know about "getting a common denominator" in order to add fractions?

Do you know that $r^2- 2r= r(r- 2)$ and that $r^2- 4= (r- 2)(r+ 2)$?

So what is a common denominator for these fractions?
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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