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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.

jjennylove Oct 19, 2018

#1**+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!

Dimitristhym Oct 19, 2018

#1**+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