(x^2-25/2x^2+5x-12)/(x^2-3x-10/x^2+9x+20)
[(x^2-25)/(2x^2+5x-12)]/[(x^2-3x-10)/(x^2+9x+20)] I think you mean
[ {(x-5)(x+5)} /{ (2x-3)(x+4) }]
/
[ {(x-5)(x+2)} / { ( x+5)(x+4) } ]
=
[ {(x-5)(x+5)} /{ (2x-3)(x+4) }] *
[{ ( x+5)(x+4) } / {(x-5)(x+2)}]
=
(x+5)^2 / [(2x-3)(x+2)]