Question

PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!! I CANNOT RETAKE THIS!!

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

Answer 1

Answer: C) x = 3, (x = 2 is an extraneous solution)

Explanation:

`(x)/(x-1)` -
`(1)/(x-2)` =
`(2x-5)/(x^(2)-3x+2)`

`(x)/(x-1)` -
`(1)/(x-2)` =
`(2x-5)/((x-1)(x-2))`

Restrictions: Denominator cannot equal zero (x - 1 ≠ 0) and (x - 2 ≠ 0), so x ≠ 1 and x ≠ 2

`(x - 1)(x - 2)(x)/(x-1)` -
`(x - 1)(x - 2)(1)/(x-2)` =
`(x - 1)(x - 2)(2x-5)/((x-1)(x-2))`

x(x - 2) - 1(x - 1) = 2x - 5

x² - 2x - x + 1 = 2x - 5

x² - 3x + 1 = 2x - 5

-2x + 5 -2x + 5

x² - 5x + 6 = 0

(x - 2)(x - 3) = 0

x - 2 = 0 x - 3 = 0

x = 2 x = 3

NOTE: x = 2 is an extraneous solution because it is one of the restricted values.