Question

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

Answer 1

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

Answer 2

Can you explain the steps? i'm lost!

Answer 3

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

Answer 4

\[\frac{x^{-1}-1}{x-1}=\frac{\frac{1}{x}-1}{x-1}=\frac{x}{x}*\frac{\frac{1}{x}-1}{x-1}=\frac{1-x}{x-1}\]

Answer 5

1-x=-(-1+x)=-(x-1)

so we have
\[\frac{1-x}\frac{-(x-1)}{x-1}=-\frac{-1}{x}\]

Answer 6

\[\frac{1-x}{x(x-1)}=\frac{-(x-1)}{x(x-1)}=\frac{-1}{x}\]

Answer 7

do you understand?

Answer 8

lol trying

Answer 9

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

Answer 10

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

Answer 11

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

Answer 12

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

Answer 13

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?

Answer 14

right

Answer 15

what are you left with?

Answer 16

-1/x

Answer 17

right except that x cannot be 1 or 0

Answer 18

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

Answer 19

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

Answer 20

thanks so much for the detailed explanation. i appreciate it

Answer 21

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

Answer 22

ok, I get it! thanks soooo much!