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Question
Solve the following equation: `("x" + 3)/("x" - 2) - (1 - "x")/"x" = 17/4`
Solution
`("x" + 3)/("x" - 2) - (1 - "x")/"x" = 17/4`
`(4"x" + 12)/("x" - 2) - (4 - 4"x")/"x" = 17`
x( 4x + 12)- ( 4 - 4x) (x-2) = 17x (x-2)
4x2 + 12x - ( 4x - 4x2 - 8+ 8x) = 17x2 -34 x
4x2 + 12x - 4x + 4x2 + 8 - 8x = 17x2 - 34x
8x2 + 8 = 17x2 - 34x
9x2 - 34x - 8 = 0
`"x"^2 - 34/9 "x" - 8/9 = 0`
`"x"^2 - 4"x" + 2/9 "x" - 8/9 = 0`
`"x"("x" - 4) + 2/9 ("x" - 4) = 0`
`("x" - 4)("x" + 2/9) = 0`
x = 4 , x = `-2/9`
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