Unable to solve QC question

Hey guys,

I tried to simplify this question using Manipulation technique, i.e, i tried to simplify the equations on both sides before substituting values.
However if i directly substitute values, i get D as the answer whereas if i substitute after simplifying i get B as the answer.

I have attached the question and my solution below.

Please help me out.

Hi ! I’m not super sure but I don’t think you can simplify in this case by dividing because it’s possible for a+b to be negative (as you’ve already proven above) and in inequalities, if you don’t know if the term is positive or negative for sure then you can’t divide them. So I do think D is right !

But in one of the classes, Greg did cancel out terms on both sides

He divided by x^2 which is always positive ! But we’re dividing by a+b which can be negative.