+1995 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.
+343 \(\frac{x}{x−1} − \frac{1}{ x−2} = \frac{2x−5 }{ x^2−3x+2}\) ,\(x≠1,x≠2\) <=> \((x-2)\frac{x}{x−1(x-2)} − (x-1)\frac{1}{(x-1) x−2} = \frac{2x−5 }{ x^2−3x+2}\)<=>\(x^2-3x+1=2x-5\) <=> \(x^2-5x+6=0\) <=>\((x-3)(x-2)=0\)
BUT \(x≠2\) SO
\(x=3\)
So correct answer is B
Hope it helps!
+343 \(\frac{x}{x−1} − \frac{1}{ x−2} = \frac{2x−5 }{ x^2−3x+2}\) ,\(x≠1,x≠2\) <=> \((x-2)\frac{x}{x−1(x-2)} − (x-1)\frac{1}{(x-1) x−2} = \frac{2x−5 }{ x^2−3x+2}\)<=>\(x^2-3x+1=2x-5\) <=> \(x^2-5x+6=0\) <=>\((x-3)(x-2)=0\)
BUT \(x≠2\) SO
\(x=3\)
So correct answer is B
Hope it helps!
