Update: I've solved the second problem, trying out the first problem now.

[ 4 - x^2 / x^2 + 7x + 12] / [2x - 4 / x + 3] = (4 - x^2)*(x+3)/[(x+3)*(x+4)*2*(x-2)], because x^2+7x+12 = (x+3)*(x+4)
cancelling x+3, and because 4 - x^2 = -(x+2)*(x-2), we can cancel the x-2 too, which gives:

= - (x+2)/(x+4)

I got what you got, except I got -x-2 / 2x+8

Unless I did something wrong, I think you left out the 2 when you factored out 2x-4?

if you are not using clear notation you make it difficult for people to help you
that is those who are not used to your messy style

methinks with "-x-2 / 2x+8" you mean "(-x-2) / (2x+8)" and not "-x-(2/2x)+8", which is what you are expressing

Er, well, it would be the first choice.