- #1
GreenLeaf
- 7
- 0
Hi all,
I've been trying to figure out why this statement is true:
[tex] \frac{r}{r+b} > \frac{r-1}{r+b-1} \quad \text{for all } b>0 [/tex]
I can't seem to reason it out. I've plugged in a few values greater than 0 and yes, it works out. But I don't understand how I can look at this and find it true.
I'm looking at it as such:
frac{r}{r} where we minus b from the denominator.
frac{r-1}{r-1} where we minus b from the denominator as well.
The only difference is that perhaps frac{r-1}{r-1} is a smaller 1 than frac{r}{r}?
If anyone could perhaps show me a more reasonable way of looking at this, I would greatly appreciate it! :)
Thanks in advance!
I've been trying to figure out why this statement is true:
[tex] \frac{r}{r+b} > \frac{r-1}{r+b-1} \quad \text{for all } b>0 [/tex]
I can't seem to reason it out. I've plugged in a few values greater than 0 and yes, it works out. But I don't understand how I can look at this and find it true.
I'm looking at it as such:
frac{r}{r} where we minus b from the denominator.
frac{r-1}{r-1} where we minus b from the denominator as well.
The only difference is that perhaps frac{r-1}{r-1} is a smaller 1 than frac{r}{r}?
If anyone could perhaps show me a more reasonable way of looking at this, I would greatly appreciate it! :)
Thanks in advance!
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