Using factorization, find the roots of the quadratic equation: + = 3 (x ≠ 2,4)

Multiplying throughout by (x - 2)(x - 4), we get
3[(x - 1)(x - 4) + (x - 2)(x - 3)] = 10(x - 2)(x – 4)
3(x ² - 5x + 4 + x ² - 5x + 6) = 10(x ² - 6x + 8)
3(2x ² - 10x + 10) = 10(x ² - 6x + 8)
6x ² - 30x + 30 = 10x ² - 60x + 80
4x ² - 30x + 50 = 0
2x ² - 15x + 25 = 0
2x ² – 10x - 5x + 25 = 0
2x(x – 5) – 5(x – 5) = 0
(2x - 5)(x - 5) = 0

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