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Question
Solve the following quadratic equation by factorisation method:
`(x + 3)/(x - 2) - (1 - x)/x = (17)/(4)`.
Solution
`(x + 3)/(x - 2) - (1 - x)/x = (17)/(4)`
⇒ `(x^2 + 3x - (x - 2) (1 - x))/(x(x- 2)) = (17)/(4)`
⇒ `(x^2 + 3x - (x - x^2 - 2 + 2x))/(x^2 - 2x) = (17)/(4)`
⇒ `(x^2 + 3x - (-x^2 + 3x - 2))/(x^2 - 2x) = (17)/(4)`
⇒ `(x^2 + 3x + x^2 - 3x + 2)/(x^2 - 2x) = (17)/(4)`
⇒ `(2x^2 + 2)/(x^2 - 2x) = (17)/(4)`
⇒ 17x2 - 34x - 8x2 + 8
⇒ 9x2 - 34x - 8 = 0
⇒ 9x2 - 36x + 2x - 8 = 0
⇒ 9x(x - 4) + 2(x - 4) = 0
⇒ (x - 4) (9x + 2) = 0
⇒ x - 4 = 0 or 9x + 2 = 0
⇒ x = 4 or x = `-(2)/(9)`.
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