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Question
Solve the following equation: `(2"x")/("x" - 4) + (2"x" - 5)/("x" - 3) = 25/3`
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Solution
`(2"x")/("x" - 4) + (2"x" - 5)/("x" - 3) = 25/3`
`(6 "x")/("x" - 4) + (6"x" - 15)/("x" - 3) = 25`
6x (x- 3)+ (6x- 15) (x- 4) = 25 (x- 4) (x-3)
6x2 -18x + 6x2 - 15x - 24x + 60 = 25 (x2 - 4x - 3x + 12)
12x2 - 57x + 60 = 25x2 - 175 x + 300
13x2 - 118 x + 240 = 0
`"x"^2 - 118/13 "x" + 240/13 = 0`
`"x"^2 - 6"x" - 40/13 "x" + 240/13 = 0`
`"x" ("x" - 6) - 40/13 ("x" - 6) = 0`
`("x" + 6)("x" - 40/13) = 0`
x = 6 , x = `40/13`
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