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Question
Solve the following equation :
`("x" - 1)/("x" - 2) + ("x" - 3)/("x" - 4) = 3 1/3`
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Solution
`("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`
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