+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 xx−1−1x−2=2x−5x2−3x+2 ,x≠1,x≠2 <=> (x−2)xx−1(x−2)−(x−1)1(x−1)x−2=2x−5x2−3x+2<=>x2−3x+1=2x−5 <=> x2−5x+6=0 <=>(x−3)(x−2)=0
BUT x≠2 SO
x=3
So correct answer is B
Hope it helps!
+343 xx−1−1x−2=2x−5x2−3x+2 ,x≠1,x≠2 <=> (x−2)xx−1(x−2)−(x−1)1(x−1)x−2=2x−5x2−3x+2<=>x2−3x+1=2x−5 <=> x2−5x+6=0 <=>(x−3)(x−2)=0
BUT x≠2 SO
x=3
So correct answer is B
Hope it helps!
