Question

Solve the following equation :

`("x" - 1)/("x" - 2) + ("x" - 3)/("x" - 4) = 3  1/3`

Answer 1

`("x" - 1)/("x" - 2) + ("x" - 3)/("x" - 4) = 3  1/3`

`(("x" - 1)("x" - 4) + ("x" - 3)("x" - 2))/(("x" - 2)("x" - 4)) = 10/3`

`("x"^2 - 5"x" + 4 + "x"^2 - 5"x" + 6)/("x"^2 - 6"x" + 8) = 10/3`

`(2"x"^2 - 10"x" + 10)/("x"^2 - 6"x" + 8) = 10/3`

6x² -30x+ 30 = 10x² - 60x + 80  

4x² - 30x + 50 = 0 

2x² - 15x + 25 = 0  

`"x"^2 - 15/2 "x" + 25/2 = 0`

`"x"^2 -5"x" - 5/2 "x" + 25/2 = 0`

`"x" ("x" - 5) - 5/2 ("x" - 5) = 0`

`("x" - 5)("x" - 5/2) = 0`

x = 5 , x = `5/2`