How would you solve this problem?

Aug 2008
2
0
(1/x-1)=1+(x/x-1)

I believe that you have to give the one the common denominator of x-1, but how do I do this while maintaining it with the other parts of the equation?

Help is appreciated.
 
Jun 2008
292
87
1/(x-1)=1+x/(x-1)
I hope this is the correct problem
it have no solution which can be proved by 2 methods
1) by inspection x<>1 (otherwise term will become undefined)
multiplying LHS ans RHS by x-1
1=x-1+x or
2x=2
or x=1 but we already know that x<>1 so no solution
2) 1/(x-1)=1+x/(x-1) or
1/(x-1)-[x/(x-1)]=1 or
(1-x)/(x-1)=1 or
-1=1 which is impossible hence no solution
 

HallsofIvy

MHF Helper
Apr 2005
20,249
7,909
If the problem is, instead, \(\displaystyle 1/(x-1)= (1+x)/(x-1)\), then, as nikhil said, x= 1 cannot be a solution. As long as x is not 1, we can multiply both sides by x-1 to get 1= 1+ x and that has solution x= 0,