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Question
Solve the following quadratic equations by factorization:
`(x-1)/(x-2)+(x-3)/(x-4)=3 1/3`, x ≠ 2, 4
Solution
We have been given
`(x-1)/(x-2)+(x-3)/(x-4)=3 1/3`
3(x2 - 5x + 4 + x2 - 5x + 6) = 10(x2 - 6x + 8)
4x2 - 30x + 50 = 0
2x2 - 15x + 25 = 0
2x2 - 10x - 5x + 25 = 0
2x(x - 5) - 5(x - 5) = 0
(2x - 5)(x - 5) = 0
Therefore,
2x - 5 = 0
2x = 5
x = 5/2
or,
x - 5 = 0
x = 5
Hence, x = 5/2 or x = 5
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