Question

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

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

Answer 1

Answer: x = 3

x = 2 is restricted (aka extraneous)

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: x - 1 ≠ 0 → x ≠ 1 and x - 2 ≠ 0 → x ≠ 2 (because the denominator cannot equal zero)

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

+2 +2 +3 +3

x = 2 x = 3 These are the solutions, but x = 2 is restricted