Question

Solve for x. xx−1−1x−2=2x−5x2−3x+2 Select each correct answer. −1 2 3 6

Answer 1

(C)x=3

Explanation:

We want to solve for x in:
`(x)/(x-1) -(1)/(x-2)=(2x-5)/(x^2-3x+2)`

Take the LCM of the Left Hand Side

`(x(x-2)-1(x-1))/((x-1)(x-2)) =(2x-5)/(x^2-3x+2)\\(x(x-2)-1(x-1))/(x^2-3x+2) =(2x-5)/(x^2-3x+2)\\$Since we have the same denominator, then:\\x(x-2)-1(x-1)=2x-5\\x^2-2x-x+1-2x+5=0\\x^2-5x+6=0\\$Factorize\\x^2-3x-2x+6=0\\x(x-3)-2(x-3)=0\\(x-3)(x-2)=0\\x-3=0$ or $x-2=0\\x=3$ or x=2`

However, substituting x=2 does not satisfy the given equation as it would make it undefined.

Therefore x=3