linda
  • linda
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
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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myininaya
  • myininaya
-1/x for x not equal to 1 or 0
linda
  • linda
Can you explain the steps? i'm lost!
myininaya
  • 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

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myininaya
  • myininaya
\[\frac{x^{-1}-1}{x-1}=\frac{\frac{1}{x}-1}{x-1}=\frac{x}{x}*\frac{\frac{1}{x}-1}{x-1}=\frac{1-x}{x-1}\]
myininaya
  • myininaya
1-x=-(-1+x)=-(x-1) so we have \[\frac{1-x}\frac{-(x-1)}{x-1}=-\frac{-1}{x}\]
myininaya
  • myininaya
\[\frac{1-x}{x(x-1)}=\frac{-(x-1)}{x(x-1)}=\frac{-1}{x}\]
myininaya
  • myininaya
do you understand?
linda
  • linda
lol trying
linda
  • linda
i see how the numerator equals 1-x after you multiplied by the x. that part I get
linda
  • linda
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
myininaya
  • myininaya
x(x-1) do you not see the corrected part a post after that post?
linda
  • linda
yes, i'm trying to put it all together.
linda
  • linda
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?
myininaya
  • myininaya
right
myininaya
  • myininaya
what are you left with?
linda
  • linda
-1/x
myininaya
  • myininaya
right except that x cannot be 1 or 0
linda
  • linda
I know it can't be 0, but why not 1?
linda
  • linda
one other problem i'm having how did 1-x turn into -(x-1) What exactly did you do to get that?
linda
  • linda
thanks so much for the detailed explanation. i appreciate it
myininaya
  • myininaya
-(x-1)=-x+1=1-x the expression before we couldn't allow x to be 1 because the denominator would be 0
linda
  • linda
ok, I get it! thanks soooo much!

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