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On factorising   2 x^{2} -3x-2 we get (x-2)(2x+1)
on factorising 2 x^{2} -5x-3 we get (x-3)(2x+1)
(2x+1) will be cancelled and we get  \frac{x-2}{x-3}
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When we solve, 2x^2-3x-2 = (2x+1)(x-2)
When we solve, 2x^2-5x-3 = (2x+1)(x-3)

Therefore, (2x+1)(x-2)/(2x+1)(x-3) = (x-2)(x-3).
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