MHB What Is a Common Denominator for These Fractions?

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SUMMARY

The discussion focuses on finding a common denominator for the fractions $\displaystyle \frac{r-1}{r^2-2r}$, $\displaystyle \frac{r-2}{r^2-4}$, and $\displaystyle \frac{-2r}{r^2-2r}$. The expressions simplify to $r(r-2)$ and $(r-2)(r+2)$, leading to the conclusion that the common denominator is $r(r-2)(r+2)$. The importance of clearly stating the full problem is emphasized to avoid confusion in mathematical discussions.

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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?
 

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