Question

Solve the following equation:

`1/("x - 1") + 2/("x" - 2) = 3/("x" - 3)`

Answer 1

`1/("x - 1") + 2/("x" - 2) = 3/("x" - 3)`

`= (1("x" - 2) + 2("x" - 1))/(("x" - 1)("x" - 2)) = 3/("x" - 3)`

`=> ("x" - 2 + 2"x" - 2)/("x"^2 - "2x" - "x" + 2) = 3/"x - 3"`

`=> (3"x" - 4)/("x"^2 - "3x" + 2) = 3/"x - 3"`

⇒ (x - 3)(3x - 4) = 3(x² - 3x + 2)

⇒ 3x² - 4x - 9x + 12 = 3x² - 9x + 6 

⇒ 3x² - 13x - 3x² + 9x = 6 - 12 

⇒ - 4x = - 6

x = `(-6)/(-4) = 3/2 = 1 1/2`