Question

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

Answer 1

Answer:

(C)x=3

Step-by-step explanation:

We want to solve for x in: $\dfrac{x}{x-1} -\dfrac{1}{x-2}=\dfrac{2x-5}{x^2-3x+2}$

Take the LCM of the Left Hand Side

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

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

Therefore x=3