simplify the rational expression

Question

3x^2-7x-20 / 12+x-x^2

I am lost on how to do this problem, any help would be apprectiated.

Answer 1

Factorise 3x^2-7x-20: (3x+5)(x-4); factorise 12+x-x^2: (4-x)(3+x), which can be written: -(x-4)(3+x), so dividing one by the other we have: (3x+5)(x-4)/(-(x-4)(3+x))=-(3x+5)/(3+x). The value x=4 is excluded because we would have zero divided by zero, which is undefinable; otherwise we can cancel the common factor x-4.