(2x^{2}-3x-2) =(2x^{2}-4x+x-2) =2x(x-2)+1(x-2) = (x-2)(2x+1)

10+x-3x^{2}= 10+6x-5x-3x^{2}= 2(5+3x)-x(5+3x)=(2-x)(5+3x) =-(x-2)(3x+5)

(2x^{2}-3x-2)/ (10+x-3x^{2})= (x-2)(2x+1)/[(x-2)(-(3x+5)]

= -(2x+1)/(3x+5)

=(-2x-1)/(3x+5)

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