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

 

1/x-1   +    2/x   =   x/x-1

 

a.  There is only one solution: x = 1.  The solution x = 2 Is an extraneous solution.

 

b.  There is only one solution:  x = 2. The solution x = 0 is an Extraneous solution.

 

c.   There is only one solution:  x = 2. The solution x = 1 is an extraneous solution.

 

d.   There are two solutions: x = 1 and x = 2.

 Oct 18, 2018
 #1
avatar+100588 
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1 / [ x - 1 ]  + 2 /x  =  x / [ x - 1]

 

get a common denominator  on both sides

 

[ x + 2 ( x - 1) ] / [ x (x - 1)]   =  x^2 / [ x (x - 1} ]

 

[3x - 2 ]  / [ x^2 - x ]   =  x^2 / [ x^2 - x ]

 

Solve for the numerators

 

3x - 2  = x^2     rearrange as

 

x^2 - 3x + 2  =  0     factor

 

(x - 2) ( x - 1)  =  0      set each factor to 0 and solve for x and we get the possible solutions

 

x  = 2    or x =1

 

Reject the second because it makes an original denominator  = 0  [ extraneous solution ]

 

"C"  is correct

 

 

cool cool cool

 Oct 18, 2018

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