## anonymous 5 years ago When x^-1 -1 is divided by x-1 what is the quotient? not sure if I wrote it clearly...in words: x to the -1 power then minus 1, then divide by x-1

1. myininaya

-1/x for x not equal to 1 or 0

2. anonymous

Can you explain the steps? i'm lost!

3. myininaya

sure (x^(-1)-1)/(x-1)=(1/x-1)/(x-1)=(1/x-1)/(x-1) * x/x=(1-x)/[x(x-1)]=-(x-1)/[x(x-1)] =-1/x

4. myininaya

$\frac{x^{-1}-1}{x-1}=\frac{\frac{1}{x}-1}{x-1}=\frac{x}{x}*\frac{\frac{1}{x}-1}{x-1}=\frac{1-x}{x-1}$

5. myininaya

1-x=-(-1+x)=-(x-1) so we have $\frac{1-x}\frac{-(x-1)}{x-1}=-\frac{-1}{x}$

6. myininaya

$\frac{1-x}{x(x-1)}=\frac{-(x-1)}{x(x-1)}=\frac{-1}{x}$

7. myininaya

do you understand?

8. anonymous

lol trying

9. anonymous

i see how the numerator equals 1-x after you multiplied by the x. that part I get

10. anonymous

the denominator is giving me trouble. when you multiply x*x-1 you got x-1 and I'm not sure why (i thought itwould be x^2-x

11. myininaya

x(x-1) do you not see the corrected part a post after that post?

12. anonymous

yes, i'm trying to put it all together.

13. anonymous

So the 1-x on top turns into -1 (x-1) and the denominator ends up as x(x-1) so therefore the (x-1) on top and bottom cancel each other out, right?

14. myininaya

right

15. myininaya

what are you left with?

16. anonymous

-1/x

17. myininaya

right except that x cannot be 1 or 0

18. anonymous

I know it can't be 0, but why not 1?

19. anonymous

one other problem i'm having how did 1-x turn into -(x-1) What exactly did you do to get that?

20. anonymous

thanks so much for the detailed explanation. i appreciate it

21. myininaya

-(x-1)=-x+1=1-x the expression before we couldn't allow x to be 1 because the denominator would be 0

22. anonymous

ok, I get it! thanks soooo much!