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Which statement best reflects the solution(s) of the equation?

 

 Feb 9, 2018
 #1
avatar+102422 
+1

1 /  [ x - 1 ]   +  2 / x    =  x / [ x - 1 ]

 

Subtract the first fraction from  both sides

 

2 / x  =     x /  [ x - 1 ]  -   1  /  [  x - 1 ]

 

2 / x  =      [ x - 1] / [ x - 1]         cross-multiply

 

2[ x - 1 ]  =   x [ x - 1 ]       simplify

 

2x  - 2  = x^2  - x            subtract 2x from both sides....add 2 to both sides

 

x^2  - 2x  - x  + 2  = 0     simplify

 

x^2 - 3x +  2  =  0        factor

 

(x - 2) ( x - 1)  =  0

 

Setting each factor to 0  and soving for x produces  x = 2  or x  = 1

 

The second solution  makes two denominators inthe original problem  = 0

 

So....x = 2  is the only solution

 

The third answer is correct

 

 

cool cool cool

 Feb 9, 2018

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