SOLUTION: 1/(x-1)^2+1/x-1=12

Question 1132643: 1/(x-1)^2+1/x-1=12
Answer by ikleyn(52781) (Show Source): You can put this solution on YOUR website!
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1/(x-1)^2+1/x-1=12
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See how I edited your post to make it unambigous:

              1/(x-1)^2 + 1/(x-1) = 12    <<<---=== I added parentheses !

Now the equation is presented clearly, and I am ready to solve it !

Solution

Introduce new variable  z = .

Then your original equation takes the form


     = 12,    or

     = 0.


Factor left side


    (z-3)*(z+4) = 0.


The two roots for z are  z= 3  and  z= -4.


Now we have two cases to analyse separately.


    Case 1.  z= 3  ====>   = 3  ====>  x-1 =   ====>  x= .


    Case 2.  z= -4  ====>   = -4  ====>  x-1 =   ====>  x= .


ANSWER.  There are two solutions  x=   and  x= .

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