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Question
Solve the following quadratic equations by factorization:
`(x+3)/(x-2)-(1-x)/x=17/4`
Solution
We have been given
`(x+3)/(x-2)-(1-x)/x=17/4`
4(x2 + 3x - x + x2 + 2 - 2x) = 17(x2 - 2x)
9x2 - 34x - 8 = 0
9x2 - 36x + 2x - 8 = 0
9x(x - 4) + 2(x - 4) = 0
(9x + 2)(x - 4) = 0
Therefore,
9x + 2 = 0
9x = -2
x = -2/9
or,
x - 4 = 0
x = 4
Hence, x = -2/9 or x = 4
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