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

x / x−1 − 1 / x−2   =   2x−5 / x^2−3x+2

 

A - There are two solutions: x = 2 and x = 3.

 

B- There is only one solution: x = 3.
The solution x = 2 is an extraneous solution.

 

C -There is only one solution: x = 3.
The solution x = 1 is an extraneous solution.

 

D - There is only one solution: x = 4.
The solution x = 1 is an extraneous solution.

 Oct 19, 2018

Best Answer 

 #1
avatar+316 
+3

\(\frac{x}{x−1} − \frac{1}{ x−2} = \frac{2x−5 }{ x^2−3x+2}\) ,\(x≠1,x≠2\) <=> \((x-2)\frac{x}{x−1(x-2)} − (x-1)\frac{1}{(x-1) x−2} = \frac{2x−5 }{ x^2−3x+2}\)<=>\(x^2-3x+1=2x-5\) <=> \(x^2-5x+6=0\) <=>\((x-3)(x-2)=0\)  

BUT  \(x≠2\) SO 

\(x=3\) 

So correct answer is B

Hope it helps! 

 Oct 19, 2018
edited by Dimitristhym  Oct 19, 2018
 #1
avatar+316 
+3
Best Answer

\(\frac{x}{x−1} − \frac{1}{ x−2} = \frac{2x−5 }{ x^2−3x+2}\) ,\(x≠1,x≠2\) <=> \((x-2)\frac{x}{x−1(x-2)} − (x-1)\frac{1}{(x-1) x−2} = \frac{2x−5 }{ x^2−3x+2}\)<=>\(x^2-3x+1=2x-5\) <=> \(x^2-5x+6=0\) <=>\((x-3)(x-2)=0\)  

BUT  \(x≠2\) SO 

\(x=3\) 

So correct answer is B

Hope it helps! 

Dimitristhym Oct 19, 2018
edited by Dimitristhym  Oct 19, 2018
 #2
avatar+708 
+2

Thank you, I appreciate the help

jjennylove  Oct 19, 2018

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