fraction multiplication

[spacewater]

r / ( r - 1 ) over r^2 / r^2 - 1

I came up with r / r for the answer but the correct answer is (r+1) / r
Can anybody out there who isnt too busy explain to me why the correct answer has +1 at the numerator?

 

[Deleted member 4993]

r / ( r - 1 ) over r^2 / r^2 - 1

I came up with r / r for the answer but the correct answer is (r+1) / r
Can anybody out there who isnt too busy explain to me why the correct answer has +1 at the numerator?

Please show your work - even if you think you are incorrect.

Hint: factorize r[sup:3mmhne8f]2[/sup:3mmhne8f] - 1 = (r + 1) (r - 1)

 

[spacewater]

the question . r / ( r - 1 ) over r^2 / r^2 - 1

i flipped r² / (r² - 1) to (r²-1 )/ r² then multiplied it by r / (r-1). i cross-canceled r and (r-1)from r / (r-1) to (r²-1)/r².

After that I got r over r

The answer sheet states otherwise. Can anybody explain to me what i did wrong? Thanks you

 

[Loren]

i flipped r² / (r² - 1) to (r²-1 )/ r² then multiplied it by r / (r-1). i cross-canceled r and (r-1)from r / (r-1) to (r²-1)/r².

\(\displaystyle \frac{r}{r-1}\cdot \frac{r^2-1}{r^2}\).

It appears that you canceled like this which is a NO! NO!. You can cancel factors, NOT terms.

\(\displaystyle \frac{r}{\rlap{/}r-\rlap{/}1}\cdot \frac{r^{\rlap{/}2}-\rlap{/}1}{r^2}\).

Try this.

\(\displaystyle \frac{r}{r-1}\cdot \frac{(r+1)(r-1)}{r^2}\)

Now, r-1 are binomial factors which can be canceled.

 

[Denis]

r / ( r - 1 ) over r^2 / r^2 - 1

Should that be r^2 / (r^2 - 1) ? If so, please be CAREFUL: no reason why you can't edit your own work :shock:

 

[Aladdin]

Ending up with Loren's work:

\(\displaystyle \frac{r+1}{r}\)