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

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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

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

BUT  $$x≠2$$ SO

$$x=3$$

Hope it helps!

Oct 19, 2018
edited by Dimitristhym  Oct 19, 2018

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

BUT  $$x≠2$$ SO

$$x=3$$